* Ribeiro et al. (2019b) L. F. R. Ribeiro, C. Gardent, and I. Gurevych.  Enhancing AMR-to-text generation with dual graph representations.  In _Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)_ , pages 3183–3194, Hong Kong, China, Nov. 2019b. Association for Computational Linguistics.  doi: 10.18653/v1/D19-1314.  URL https://www.aclweb.org/anthology/D19-1314.
  * Riedel et al. (2010) S. Riedel, L. Yao, and A. McCallum.  Modeling relations and their mentions without labeled text.  In _Joint European Conference on Machine Learning and Knowledge Discovery in Databases_ , pages 148–163. Springer, 2010.
  * Sachan et al. (2020) D. S. Sachan, L. Wu, M. Sachan, and W. Hamilton.  Stronger transformers for neural multi-hop question generation.  _arXiv preprint arXiv:2010.11374_ , 2020.
  * Sagae and Lavie (2005) K. Sagae and A. Lavie.  A classifier-based parser with linear run-time complexity.  In _Proceedings of the Ninth International Workshop on Parsing Technology_ , pages 125–132, Vancouver, British Columbia, Oct. 2005. Association for Computational Linguistics.  URL https://www.aclweb.org/anthology/W05-1513.
  * Sahu et al. (2019) S. K. Sahu, F. Christopoulou, M. Miwa, and S. Ananiadou.  Inter-sentence relation extraction with document-level graph convolutional neural network.  In _Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics_ , pages 4309–4316, Florence, Italy, July 2019. Association for Computational Linguistics.  doi: 10.18653/v1/P19-1423.  URL https://www.aclweb.org/anthology/P19-1423.
  * Sandhaus (2008) E. Sandhaus.  The New York Times Annotated Corpus.  2008\.  doi: 11272.1/AB2/GZC6PL.  URL https://hdl.handle.net/11272.1/AB2/GZC6PL.
  * Santoro et al. (2017) A. Santoro, D. Raposo, D. G. Barrett, M. Malinowski, R. Pascanu, P. Battaglia, and T. Lillicrap.  A simple neural network module for relational reasoning.  In _Proceedings of the 31st International Conference on Neural Information Processing Systems_ , pages 4974–4983, 2017.
  * Saxena et al. (2020) A. Saxena, A. Tripathi, and P. Talukdar.  Improving multi-hop question answering over knowledge graphs using knowledge base embeddings.  In _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics_ , pages 4498–4507, Online, July 2020. Association for Computational Linguistics.  doi: 10.18653/v1/2020.acl-main.412.  URL https://www.aclweb.org/anthology/2020.acl-main.412.
  * Schlichtkrull et al. (2018) M. Schlichtkrull, T. N. Kipf, P. Bloem, R. Van Den Berg, I. Titov, and M. Welling.  Modeling relational data with graph convolutional networks.  In _European Semantic Web Conference_ , pages 593–607. Springer, 2018\.
  * Schuster and Paliwal (1997) M. Schuster and K. K. Paliwal.  Bidirectional recurrent neural networks.  _IEEE Transactions on Signal Processing_ , 45(11):2673–2681, 1997.  doi: 10.1109/78.650093.
  * See et al. (2017) A. See, P. J. Liu, and C. D. Manning.  Get to the point: Summarization with pointer-generator networks.  In _Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pages 1073–1083, 2017\.
  * Seo et al. (2017) M. J. Seo, A. Kembhavi, A. Farhadi, and H. Hajishirzi.  Bidirectional attention flow for machine comprehension.  In _5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings_. OpenReview.net, 2017.  URL https://openreview.net/forum?id=HJ0UKP9ge.
  * Serban et al. (2016) I. Serban, A. Sordoni, Y. Bengio, A. Courville, and J. Pineau.  Building end-to-end dialogue systems using generative hierarchical neural network models.  In _Proceedings of the AAAI Conference on Artificial Intelligence_ , volume 30, 2016.
  * Serban et al. (2017) I. Serban, A. Sordoni, R. Lowe, L. Charlin, J. Pineau, A. Courville, and Y. Bengio.  A hierarchical latent variable encoder-decoder model for generating dialogues.  In _Proceedings of the AAAI Conference on Artificial Intelligence_ , volume 31, 2017.
  * Shang et al. (2019) C. Shang, Y. Tang, J. Huang, J. Bi, X. He, and B. Zhou.  End-to-end structure-aware convolutional networks for knowledge base completion.  In _Proceedings of the AAAI Conference on Artificial Intelligence_ , volume 33, pages 3060–3067, 2019.
  * Shao et al. (2020) B. Shao, Y. Gong, W. Qi, G. Cao, J. Ji, and X. Lin.  Graph-based transformer with cross-candidate verification for semantic parsing.  _Proceedings of the AAAI Conference on Artificial Intelligence_ , 34(05):8807–8814, Apr. 2020.  doi: 10.1609/aaai.v34i05.6408.  URL https://ojs.aaai.org/index.php/AAAI/article/view/6408.
  * Shaw et al. (2018) P. Shaw, J. Uszkoreit, and A. Vaswani.  Self-attention with relative position representations.  In _Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 2 (Short Papers)_ , pages 464–468, New Orleans, Louisiana, June 2018. Association for Computational Linguistics.  doi: 10.18653/v1/N18-2074.  URL https://www.aclweb.org/anthology/N18-2074.
  * Shen and Lapata (2007) D. Shen and M. Lapata.  Using semantic roles to improve question answering.  In _Proceedings of the 2007 joint conference on empirical methods in natural language processing and computational natural language learning (EMNLP-CoNLL)_ , pages 12–21, 2007.
  * Shen et al. (2021) Z. Shen, M. Zhang, H. Zhao, S. Yi, and H. Li.  Efficient attention: Attention with linear complexities.  In _Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision_ , pages 3531–3539, 2021.
  * Shi et al. (2020) C. Shi, M. Xu, H. Guo, M. Zhang, and J. Tang.  A graph to graphs framework for retrosynthesis prediction.  In _International Conference on Machine Learning_ , pages 8818–8827. PMLR, 2020.
  * Simonovsky and Komodakis (2017) M. Simonovsky and N. Komodakis.  Dynamic edge-conditioned filters in convolutional neural networks on graphs.  In _Proceedings of the IEEE conference on computer vision and pattern recognition_ , pages 3693–3702, 2017.
  * Song et al. (2017) L. Song, X. Peng, Y. Zhang, Z. Wang, and D. Gildea.  Amr-to-text generation with synchronous node replacement grammar.  In _Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers)_ , pages 7–13, 2017.
  * Song et al. (2018a) L. Song, Z. Wang, W. Hamza, Y. Zhang, and D. Gildea.  Leveraging context information for natural question generation.  In _Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 2 (Short Papers)_ , pages 569–574, 2018a.
  * Song et al. (2018b) L. Song, Z. Wang, M. Yu, Y. Zhang, R. Florian, and D. Gildea.  Exploring graph-structured passage representation for multi-hop reading comprehension with graph neural networks.  _arXiv preprint arXiv:1809.02040_ , 2018b.
  * Song et al. (2018c) L. Song, Y. Zhang, Z. Wang, and D. Gildea.  A graph-to-sequence model for AMR-to-text generation.  In _Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pages 1616–1626, Melbourne, Australia, July 2018c. Association for Computational Linguistics.  doi: 10.18653/v1/P18-1150.  URL https://www.aclweb.org/anthology/P18-1150.
  * Song et al. (2018d) L. Song, Y. Zhang, Z. Wang, and D. Gildea.  N-ary relation extraction using graph-state LSTM.  In _Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing_ , pages 2226–2235, Brussels, Belgium, Oct.-Nov. 2018d. Association for Computational Linguistics.  doi: 10.18653/v1/D18-1246.  URL https://www.aclweb.org/anthology/D18-1246.
  * Song et al. (2018e) L. Song, Y. Zhang, Z. Wang, and D. Gildea.  A graph-to-sequence model for amr-to-text generation.  _arXiv preprint arXiv:1805.02473_ , 2018e.
  * Song et al. (2019) L. Song, D. Gildea, Y. Zhang, Z. Wang, and J. Su.  Semantic neural machine translation using amr.  _Transactions of the Association for Computational Linguistics_ , 7:19–31, 2019.
  * Song et al. (2020) L. Song, A. Wang, J. Su, Y. Zhang, K. Xu, Y. Ge, and D. Yu.  Structural information preserving for graph-to-text generation.  In _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics_ , pages 7987–7998, Online, July 2020. Association for Computational Linguistics.  doi: 10.18653/v1/2020.acl-main.712.  URL https://www.aclweb.org/anthology/2020.acl-main.712.
  * Sorokin and Gurevych (2018a) D. Sorokin and I. Gurevych.  Modeling semantics with gated graph neural networks for knowledge base question answering.  In E. M. Bender, L. Derczynski, and P. Isabelle, editors, _Proceedings of the 27th International Conference on Computational Linguistics, COLING 2018, Santa Fe, New Mexico, USA, August 20-26, 2018_ , pages 3306–3317. Association for Computational Linguistics, 2018a.
  * Sorokin and Gurevych (2018b) D. Sorokin and I. Gurevych.  Modeling semantics with gated graph neural networks for knowledge base question answering.  _arXiv preprint arXiv:1808.04126_ , 2018b.
  * Speer et al. (2017) R. Speer, J. Chin, and C. Havasi.  Conceptnet 5.5: An open multilingual graph of general knowledge.  In _Proceedings of the AAAI Conference on Artificial Intelligence_ , volume 31, 2017.
  * Su et al. (2020) D. Su, Y. Xu, W. Dai, Z. Ji, T. Yu, and P. Fung.  Multi-hop question generation with graph convolutional network.  In _Findings of the Association for Computational Linguistics: EMNLP 2020_ , pages 4636–4647, Online, Nov. 2020. Association for Computational Linguistics.  doi: 10.18653/v1/2020.findings-emnlp.416.  URL https://www.aclweb.org/anthology/2020.findings-emnlp.416.
  * Suchanek et al. (2008) F. M. Suchanek, G. Kasneci, and G. Weikum.  Yago: A large ontology from wikipedia and wordnet.  _Journal of Web Semantics_ , 6(3):203–217, 2008\.
  * Sui et al. (2019) D. Sui, Y. Chen, K. Liu, J. Zhao, and S. Liu.  Leverage lexical knowledge for chinese named entity recognition via collaborative graph network.  In _Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)_ , pages 3821–3831, 2019.
  * Sukhbaatar et al. (2015) S. Sukhbaatar, A. Szlam, J. Weston, and R. Fergus.  End-to-end memory networks.  In _Proceedings of the 28th International Conference on Neural Information Processing Systems-Volume 2_ , pages 2440–2448, 2015.
  * Sun et al. (2019a) C. Sun, Y. Gong, Y. Wu, M. Gong, D. Jiang, M. Lan, S. Sun, and N. Duan.  Joint type inference on entities and relations via graph convolutional networks.  In _Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics_ , pages 1361–1370, Florence, Italy, July 2019a. Association for Computational Linguistics.  doi: 10.18653/v1/P19-1131.  URL https://www.aclweb.org/anthology/P19-1131.
  * Sun et al. (2018a) H. Sun, B. Dhingra, M. Zaheer, K. Mazaitis, R. Salakhutdinov, and W. Cohen.  Open domain question answering using early fusion of knowledge bases and text.  In _Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing_ , pages 4231–4242, Brussels, Belgium, Oct.-Nov. 2018a. Association for Computational Linguistics.  doi: 10.18653/v1/D18-1455.  URL https://www.aclweb.org/anthology/D18-1455.
  * Sun et al. (2019b) H. Sun, T. Bedrax-Weiss, and W. Cohen.  PullNet: Open domain question answering with iterative retrieval on knowledge bases and text.  In _Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)_ , pages 2380–2390, Hong Kong, China, Nov. 2019b. Association for Computational Linguistics.  doi: 10.18653/v1/D19-1242.  URL https://www.aclweb.org/anthology/D19-1242.
  * Sun et al. (2019c) K. Sun, R. Zhang, S. Mensah, Y. Mao, and X. Liu.  Aspect-level sentiment analysis via convolution over dependency tree.  In _Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)_ , pages 5679–5688, Hong Kong, China, Nov. 2019c. Association for Computational Linguistics.  doi: 10.18653/v1/D19-1569.  URL https://www.aclweb.org/anthology/D19-1569.
  * Sun et al. (2011) Y. Sun, J. Han, X. Yan, P. S. Yu, and T. Wu.  Pathsim: Meta path-based top-k similarity search in heterogeneous information networks.  _Proceedings of the VLDB Endowment_ , 4(11):992–1003, 2011.
  * Sun et al. (2017) Z. Sun, W. Hu, and C. Li.  Cross-lingual entity alignment via joint attribute-preserving embedding.  In _International Semantic Web Conference_ , pages 628–644. Springer, 2017.
  * Sun et al. (2018b) Z. Sun, W. Hu, Q. Zhang, and Y. Qu.  Bootstrapping entity alignment with knowledge graph embedding.  In _IJCAI_ , volume 18, pages 4396–4402, 2018b.
  * Sun et al. (2020a) Z. Sun, C. Wang, W. Hu, M. Chen, J. Dai, W. Zhang, and Y. Qu.  Knowledge graph alignment network with gated multi-hop neighborhood aggregation.  In _Proceedings of the AAAI Conference on Artificial Intelligence_ , volume 34, pages 222–229, 2020a.
  * Sun et al. (2020b) Z. Sun, Q. Zhu, Y. Xiong, Y. Sun, L. Mou, and L. Zhang.  Treegen: A tree-based transformer architecture for code generation.  In _Proceedings of the AAAI Conference on Artificial Intelligence_ , volume 34, pages 8984–8991, 2020b.
  * Sutskever et al. (2014) I. Sutskever, O. Vinyals, and Q. V. Le.  Sequence to sequence learning with neural networks.  In Z. Ghahramani, M. Welling, C. Cortes, N. D. Lawrence, and K. Q. Weinberger, editors, _Advances in Neural Information Processing Systems 27: Annual Conference on Neural Information Processing Systems 2014, December 8-13 2014, Montreal, Quebec, Canada_ , pages 3104–3112, 2014.  URL https://proceedings.neurips.cc/paper/2014/hash/a14ac55a4f27472c5d894ec1c3c743d2-Abstract.html.
  * Tai et al. (2015) K. S. Tai, R. Socher, and C. D. Manning.  Improved semantic representations from tree-structured long short-term memory networks.  In _Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language Processing (Volume 1: Long Papers)_ , pages 1556–1566, 2015.
  * Talmor and Berant (2018) A. Talmor and J. Berant.  The web as a knowledge-base for answering complex questions.  In _Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long Papers)_ , pages 641–651, 2018.
  * Talmor et al. (2019) A. Talmor, J. Herzig, N. Lourie, and J. Berant.  Commonsenseqa: A question answering challenge targeting commonsense knowledge.  In _NAACL-HLT (1)_ , 2019.
  * Tang et al. (2016) D. Tang, B. Qin, X. Feng, and T. Liu.  Effective lstms for target-dependent sentiment classification.  In _Proceedings of COLING 2016, the 26th International Conference on Computational Linguistics: Technical Papers_ , pages 3298–3307, 2016\.
  * Tang et al. (2020a) H. Tang, D. Ji, C. Li, and Q. Zhou.  Dependency graph enhanced dual-transformer structure for aspect-based sentiment classification.  In _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics_ , pages 6578–6588, Online, July 2020a. Association for Computational Linguistics.  doi: 10.18653/v1/2020.acl-main.588.  URL https://www.aclweb.org/anthology/2020.acl-main.588.
  * Tang et al. (2015) J. Tang, M. Qu, and Q. Mei.  Pte: Predictive text embedding through large-scale heterogeneous text networks.  In _Proceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining_ , pages 1165–1174, 2015.
  * Tang et al. (2020b) Z. Tang, Y. Shen, X. Ma, W. Xu, J. Yu, and W. Lu.  Multi-hop reading comprehension across documents with path-based graph convolutional network.  In C. Bessiere, editor, _Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, IJCAI 2020_ , pages 3905–3911. ijcai.org, 2020b.
  * Tang et al. (2020c) Z. Tang, Y. Shen, X. Ma, W. Xu, J. Yu, and W. Lu.  Multi-hop reading comprehension across documents with path-based graph convolutional network.  _arXiv preprint arXiv:2006.06478_ , 2020c.
  * Tarau et al. (2005) P. Tarau, R. Mihalcea, and E. Figa.  Semantic document engineering with wordnet and pagerank.  In _Proceedings of the 2005 ACM symposium on Applied computing_ , pages 782–786, 2005.
  * Taylor et al. (2003) A. Taylor, M. Marcus, and B. Santorini.  The penn treebank: an overview.  _Treebanks_ , pages 5–22, 2003.
  * Teru et al. (2020) K. Teru, E. Denis, and W. Hamilton.  Inductive relation prediction by subgraph reasoning.  In _International Conference on Machine Learning_ , pages 9448–9457. PMLR, 2020.
  * Thayaparan et al. (2019) M. Thayaparan, M. Valentino, V. Schlegel, and A. Freitas.  Identifying supporting facts for multi-hop question answering with document graph networks.  In _Proceedings of the Thirteenth Workshop on Graph-Based Methods for Natural Language Processing (TextGraphs-13)_ , pages 42–51, Hong Kong, Nov. 2019. Association for Computational Linguistics.  doi: 10.18653/v1/D19-5306.  URL https://www.aclweb.org/anthology/D19-5306.
  * Thompson (2017) A. Thompson.  All the news: 143,000 articles from 15 american publications, 2017.
  * Toutanova et al. (2015) K. Toutanova, D. Chen, P. Pantel, H. Poon, P. Choudhury, and M. Gamon.  Representing text for joint embedding of text and knowledge bases.  In _Proceedings of the 2015 conference on empirical methods in natural language processing_ , pages 1499–1509, 2015.
  * Trischler et al. (2017) A. Trischler, T. Wang, X. Yuan, J. Harris, A. Sordoni, P. Bachman, and K. Suleman.  Newsqa: A machine comprehension dataset.  In _Proceedings of the 2nd Workshop on Representation Learning for NLP_ , pages 191–200, 2017.
  * Trouillon et al. (2016) T. Trouillon, J. Welbl, S. Riedel, É. Gaussier, and G. Bouchard.  Complex embeddings for simple link prediction.  In _International Conference on Machine Learning_ , pages 2071–2080. PMLR, 2016.
  * Tsai et al. (2019) Y.-H. H. Tsai, S. Bai, M. Yamada, L.-P. Morency, and R. Salakhutdinov.  Transformer dissection: An unified understanding for transformer’s attention via the lens of kernel.  In _Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)_ , pages 4335–4344, 2019.
  * Tu et al. (2019a) M. Tu, G. Wang, J. Huang, Y. Tang, X. He, and B. Zhou.  Multi-hop reading comprehension across multiple documents by reasoning over heterogeneous graphs.  In A. Korhonen, D. R. Traum, and L. Màrquez, editors, _Proceedings of the 57th Conference of the Association for Computational Linguistics, ACL 2019, Florence, Italy, July 28- August 2, 2019, Volume 1: Long Papers_ , pages 2704–2713. Association for Computational Linguistics, 2019a.
  * Tu et al. (2019b) M. Tu, G. Wang, J. Huang, Y. Tang, X. He, and B. Zhou.  Multi-hop reading comprehension across multiple documents by reasoning over heterogeneous graphs.  In _Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics_ , pages 2704–2713, Florence, Italy, July 2019b. Association for Computational Linguistics.  doi: 10.18653/v1/P19-1260.  URL https://www.aclweb.org/anthology/P19-1260.
  * Tu et al. (2016) Z. Tu, Z. Lu, Y. Liu, X. Liu, and H. Li.  Modeling coverage for neural machine translation.  _arXiv preprint arXiv:1601.04811_ , 2016.
  * Usbeck et al. (2017) R. Usbeck, A.-C. N. Ngomo, B. Haarmann, A. Krithara, M. Röder, and G. Napolitano.  7th open challenge on question answering over linked data (qald-7).  In _Semantic web evaluation challenge_ , pages 59–69. Springer, 2017\.
  * Vashishth et al. (2018) S. Vashishth, R. Joshi, S. S. Prayaga, C. Bhattacharyya, and P. Talukdar.  RESIDE: Improving distantly-supervised neural relation extraction using side information.  In _Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing_ , pages 1257–1266, Brussels, Belgium, Oct.-Nov. 2018\. Association for Computational Linguistics.  doi: 10.18653/v1/D18-1157.  URL https://www.aclweb.org/anthology/D18-1157.
  * Vashishth et al. (2019) S. Vashishth, S. Sanyal, V. Nitin, and P. Talukdar.  Composition-based multi-relational graph convolutional networks.  _arXiv preprint arXiv:1911.03082_ , 2019.
  * Vaswani et al. (2017) A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser, and I. Polosukhin.  Attention is all you need.  In _NIPS_ , 2017.
  * Velickovic et al. (2018) P. Velickovic, G. Cucurull, A. Casanova, A. Romero, P. Liò, and Y. Bengio.  Graph attention networks.  In _6th International Conference on Learning Representations_ , 2018\.
  * Velickovic et al. (2020) P. Velickovic, L. Buesing, M. C. Overlan, R. Pascanu, O. Vinyals, and C. Blundell.  Pointer graph networks.  In _Advances in Neural Information Processing Systems_ , 2020.
  * Vinyals et al. (2015) O. Vinyals, M. Fortunato, and N. Jaitly.  Pointer networks.  In _Advances in Neural Information Processing Systems_ , pages 2692–2700, 2015.
  * Vinyals et al. (2016) O. Vinyals, S. Bengio, and M. Kudlur.  Order matters: Sequence to sequence for sets.  In Y. Bengio and Y. LeCun, editors, _4th International Conference on Learning Representations, ICLR 2016, San Juan, Puerto Rico, May 2-4, 2016, Conference Track Proceedings_ , 2016.  URL http://arxiv.org/abs/1511.06391.
  * Vitale et al. (2012) D. Vitale, P. Ferragina, and U. Scaiella.  Classification of short texts by deploying topical annotations.  In _European Conference on Information Retrieval_ , pages 376–387. Springer, 2012.
  * Wan et al. (2016) S. Wan, Y. Lan, J. Guo, J. Xu, L. Pang, and X. Cheng.  A deep architecture for semantic matching with multiple positional sentence representations.  In _Proceedings of the AAAI Conference on Artificial Intelligence_ , volume 30, 2016.
  * Wang et al. (2020a) D. Wang, P. Liu, Y. Zheng, X. Qiu, and X. Huang.  Heterogeneous graph neural networks for extractive document summarization.  In _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics_ , pages 6209–6219, Online, July 2020a. Association for Computational Linguistics.  doi: 10.18653/v1/2020.acl-main.553.  URL https://www.aclweb.org/anthology/2020.acl-main.553.
  * Wang et al. (2019a) H. Wang, S. Li, R. Pan, and M. Mao.  Incorporating graph attention mechanism into knowledge graph reasoning based on deep reinforcement learning.  In _Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)_ , pages 2623–2631, Hong Kong, China, Nov. 2019a. Association for Computational Linguistics.  doi: 10.18653/v1/D19-1264.  URL https://www.aclweb.org/anthology/D19-1264.
  * Wang et al. (2020b) K. Wang, W. Shen, Y. Yang, X. Quan, and R. Wang.  Relational Graph Attention Network for Aspect-based Sentiment Analysis.  In _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics_ , pages 3229–3238, Online, July 2020b. Association for Computational Linguistics.  doi: 10.18653/v1/2020.acl-main.295.  URL https://www.aclweb.org/anthology/2020.acl-main.295.
  * Wang et al. (2020c) L. Wang, Z. Xu, Z. Lin, H. Zheng, and Y. Shen.  Answer-driven deep question generation based on reinforcement learning.  In D. Scott, N. Bel, and C. Zong, editors, _Proceedings of the 28th International Conference on Computational Linguistics, COLING 2020, Barcelona, Spain (Online), December 8-13, 2020_ , pages 5159–5170. International Committee on Computational Linguistics, 2020c.
  * Wang et al. (2020d) L. Wang, Z. Xu, Z. Lin, H. Zheng, and Y. Shen.  Answer-driven deep question generation based on reinforcement learning.  In _Proceedings of the 28th International Conference on Computational Linguistics_ , pages 5159–5170, Barcelona, Spain (Online), Dec. 2020d. International Committee on Computational Linguistics.  doi: 10.18653/v1/2020.coling-main.452.  URL https://www.aclweb.org/anthology/2020.coling-main.452.
  * Wang et al. (2019b) M. Wang, L. Yu, D. Zheng, Q. Gan, Y. Gai, Z. Ye, M. Li, J. Zhou, Q. Huang, C. Ma, et al.  Deep graph library: Towards efficient and scalable deep learning on graphs.  2019b.
  * Wang et al. (2019c) P. Wang, J. Han, C. Li, and R. Pan.  Logic attention based neighborhood aggregation for inductive knowledge graph embedding.  In _Proceedings of the AAAI Conference on Artificial Intelligence_ , volume 33, pages 7152–7159, 2019c.
  * Wang et al. (2019d) R. Wang, D. Zhou, and Y. He.  Atm: Adversarial-neural topic model.  _Information Processing & Management_, 56(6):102098, 2019d.
  * Wang et al. (2020e) S. Wang, B. Z. Li, M. Khabsa, H. Fang, and H. Ma.  Linformer: Self-attention with linear complexity.  _CoRR_ , abs/2006.04768, 2020e.  URL https://arxiv.org/abs/2006.04768.
  * Wang et al. (2020f) T. Wang, X. Wan, and H. Jin.  Amr-to-text generation with graph transformer.  _Transactions of the Association for Computational Linguistics_ , 8:19–33, 2020f.
  * Wang et al. (2020g) T. Wang, X. Wan, and S. Yao.  Better amr-to-text generation with graph structure reconstruction.  In C. Bessiere, editor, _Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, IJCAI-20_ , pages 3919–3925. International Joint Conferences on Artificial Intelligence Organization, 7 2020g.  Main track.
  * Wang et al. (2019e) X. Wang, H. Ji, C. Shi, B. Wang, Y. Ye, P. Cui, and P. S. Yu.  Heterogeneous graph attention network.  In _The World Wide Web Conference_ , pages 2022–2032, 2019e.
  * Wang et al. (2019f) X. Wang, P. Kapanipathi, R. Musa, M. Yu, K. Talamadupula, I. Abdelaziz, M. Chang, A. Fokoue, B. Makni, N. Mattei, and M. Witbrock.  Improving natural language inference using external knowledge in the science questions domain.  _Proceedings of the AAAI Conference on Artificial Intelligence_ , 33(01):7208–7215, Jul. 2019f.  doi: 10.1609/aaai.v33i01.33017208.  URL https://ojs.aaai.org/index.php/AAAI/article/view/4705.
  * Wang et al. (2017) Y. Wang, X. Liu, and S. Shi.  Deep neural solver for math word problems.  In _Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing_ , pages 845–854, 2017.
  * Wang et al. (2018) Z. Wang, Q. Lv, X. Lan, and Y. Zhang.  Cross-lingual knowledge graph alignment via graph convolutional networks.  In _Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing_ , pages 349–357, 2018.
  * Wang et al. (2019g) Z. Wang, Z. Ren, C. He, P. Zhang, and Y. Hu.  Robust embedding with multi-level structures for link prediction.  In _IJCAI_ , pages 5240–5246, 2019g.
  * Wang et al. (2020h) Z. Wang, J. Yang, and X. Ye.  Knowledge graph alignment with entity-pair embedding.  In _Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP)_ , pages 1672–1680, Online, Nov. 2020h. Association for Computational Linguistics.  doi: 10.18653/v1/2020.emnlp-main.130.  URL https://www.aclweb.org/anthology/2020.emnlp-main.130.
  * Welbl et al. (2018) J. Welbl, P. Stenetorp, and S. Riedel.  Constructing datasets for multi-hop reading comprehension across documents.  _Transactions of the Association for Computational Linguistics_ , 6:287–302, 2018.
  * Williams et al. (2018) A. Williams, N. Nangia, and S. Bowman.  A broad-coverage challenge corpus for sentence understanding through inference.  _Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long Papers)_ , 2018.  doi: 10.18653/v1/n18-1101.  URL http://dx.doi.org/10.18653/v1/N18-1101.
  * Williams et al. (2014) J. D. Williams, M. Henderson, A. Raux, B. Thomson, A. Black, and D. Ramachandran.  The dialog state tracking challenge series.  _AI Magazine_ , 35(4):121–124, 2014.
  * Williams (1992) R. J. Williams.  Simple statistical gradient-following algorithms for connectionist reinforcement learning.  _Machine learning_ , 8(3-4):229–256, 1992.
  * Wu et al. (2020a) J. Wu, M. Cao, J. C. K. Cheung, and W. L. Hamilton.  TeMP: Temporal message passing for temporal knowledge graph completion.  In _Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP)_ , pages 5730–5746, Online, Nov. 2020a. Association for Computational Linguistics.  doi: 10.18653/v1/2020.emnlp-main.462.  URL https://www.aclweb.org/anthology/2020.emnlp-main.462.
  * Wu et al. (2020b) Q. Wu, Q. Zhang, J. Fu, and X. Huang.  A knowledge-aware sequence-to-tree network for math word problem solving.  In _Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP)_ , pages 7137–7146, Online, Nov. 2020b. Association for Computational Linguistics.  doi: 10.18653/v1/2020.emnlp-main.579.  URL https://www.aclweb.org/anthology/2020.emnlp-main.579.
  * Wu et al. (2019a) Y. Wu, X. Liu, Y. Feng, Z. Wang, R. Yan, and D. Zhao.  Relation-aware entity alignment for heterogeneous knowledge graphs.  In _Proceedings of the 28th International Joint Conference on Artificial Intelligence_ , pages 5278–5284. AAAI Press, 2019a.
  * Wu et al. (2019b) Y. Wu, X. Liu, Y. Feng, Z. Wang, and D. Zhao.  Jointly learning entity and relation representations for entity alignment.  In _Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)_ , pages 240–249, 2019b.
  * Wu et al. (2020c) Z. Wu, R. Koncel-Kedziorski, M. Ostendorf, and H. Hajishirzi.  Extracting summary knowledge graphs from long documents.  _arXiv preprint arXiv:2009.09162_ , 2020c.
  * Xia et al. (2019) M. Xia, G. Huang, L. Liu, and S. Shi.  Graph based translation memory for neural machine translation.  _Proceedings of the AAAI Conference on Artificial Intelligence_ , 33(01):7297–7304, Jul. 2019.  doi: 10.1609/aaai.v33i01.33017297.  URL https://ojs.aaai.org/index.php/AAAI/article/view/4716.
  * Xia et al. (2020) Q. Xia, R. Wang, Z. Li, Y. Zhang, and M. Zhang.  Semantic role labeling with heterogeneous syntactic knowledge.  In _Proceedings of the 28th International Conference on Computational Linguistics_ , pages 2979–2990, 2020.
  * Xiao et al. (2019) F. Xiao, J. Li, H. Zhao, R. Wang, and K. Chen.  Lattice-based transformer encoder for neural machine translation.  In _Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics_ , pages 3090–3097, Florence, Italy, July 2019. Association for Computational Linguistics.  doi: 10.18653/v1/P19-1298.  URL https://www.aclweb.org/anthology/P19-1298.
  * Xie et al. (2020) Z. Xie, G. Zhou, J. Liu, and X. Huang.  Reinceptione: Relation-aware inception network with joint local-global structural information for knowledge graph embedding.  In _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics_ , pages 5929–5939, 2020.
  * Xiong et al. (2017a) C. Xiong, V. Zhong, and R. Socher.  Dynamic coattention networks for question answering.  In _5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings_. OpenReview.net, 2017a.  URL https://openreview.net/forum?id=rJeKjwvclx.
  * Xiong et al. (2017b) W. Xiong, T. Hoang, and W. Y. Wang.  Deeppath: A reinforcement learning method for knowledge graph reasoning.  In _Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing_ , pages 564–573, 2017b.
  * Xu et al. (2020a) J. Xu, Z. Gan, Y. Cheng, and J. Liu.  Discourse-aware neural extractive text summarization.  In _Proceedings of the 58th annual meeting of the association for computational linguistics_ , pages 5021–5031, 2020a.
  * Xu et al. (2018a) K. Xu, L. Wu, Z. Wang, Y. Feng, and V. Sheinin.  SQL-to-text generation with graph-to-sequence model.  In _Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing_ , pages 931–936, Brussels, Belgium, Oct.-Nov. 2018a. Association for Computational Linguistics.  doi: 10.18653/v1/D18-1112.  URL https://www.aclweb.org/anthology/D18-1112.
  * Xu et al. (2018b) K. Xu, L. Wu, Z. Wang, Y. Feng, M. Witbrock, and V. Sheinin.  Graph2seq: Graph to sequence learning with attention-based neural networks.  _arXiv preprint arXiv:1804.00823_ , 2018b.
  * Xu et al. (2018c) K. Xu, L. Wu, Z. Wang, M. Yu, L. Chen, and V. Sheinin.  Exploiting rich syntactic information for semantic parsing with graph-to-sequence model.  In _Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing_ , pages 918–924, Brussels, Belgium, Oct.-Nov. 2018c. Association for Computational Linguistics.  doi: 10.18653/v1/D18-1110.  URL https://www.aclweb.org/anthology/D18-1110.
  * Xu et al. (2019a) K. Xu, L. Wang, M. Yu, Y. Feng, Y. Song, Z. Wang, and D. Yu.  Cross-lingual knowledge graph alignment via graph matching neural network.  In _Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics_ , pages 3156–3161, Florence, Italy, July 2019a. Association for Computational Linguistics.  doi: 10.18653/v1/P19-1304.  URL https://www.aclweb.org/anthology/P19-1304.
  * Xu et al. (2020b) K. Xu, L. Song, Y. Feng, Y. Song, and D. Yu.  Coordinated reasoning for cross-lingual knowledge graph alignment.  _arXiv preprint arXiv:2001.08728_ , 2020b.
  * Xu et al. (2020c) M. Xu, L. Li, D. F. Wai, Q. Liu, and L. S. Chao.  Document graph for neural machine translation.  _ArXiv_ , abs/2012.03477, 2020c.
  * Xu et al. (2019b) X. Xu, W. Feng, Y. Jiang, X. Xie, Z. Sun, and Z.-H. Deng.  Dynamically pruned message passing networks for large-scale knowledge graph reasoning.  _arXiv preprint arXiv:1909.11334_ , 2019b.
  * Yan et al. (2019) H. Yan, X. Jin, X. Meng, J. Guo, and X. Cheng.  Event detection with multi-order graph convolution and aggregated attention.  In _Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)_ , pages 5766–5770, Hong Kong, China, Nov. 2019. Association for Computational Linguistics.  doi: 10.18653/v1/D19-1582.  URL https://www.aclweb.org/anthology/D19-1582.
  * Yang et al. (2014) B. Yang, W.-t. Yih, X. He, J. Gao, and L. Deng.  Embedding entities and relations for learning and inference in knowledge bases.  _arXiv preprint arXiv:1412.6575_ , 2014.
  * Yang et al. (2019) H.-W. Yang, Y. Zou, P. Shi, W. Lu, J. Lin, and S. Xu.  Aligning cross-lingual entities with multi-aspect information.  In _Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)_ , pages 4422–4432, 2019.
  * Yang and Deng (2020) K. Yang and J. Deng.  Strongly incremental constituency parsing with graph neural networks.  _arXiv preprint arXiv:2010.14568_ , 2020.
  * Yang et al. (2016) L. Yang, Q. Ai, J. Guo, and W. B. Croft.  anmm: Ranking short answer texts with attention-based neural matching model.  In _Proceedings of the 25th ACM international on conference on information and knowledge management_ , pages 287–296, 2016.
  * Yang et al. (2020) L. Yang, F. Wu, J. Gu, C. Wang, X. Cao, D. Jin, and Y. Guo.  Graph Attention Topic Modeling Network.  In _Proceedings of The Web Conference 2020_ , WWW ’20, pages 144–154, New York, NY, USA, Apr. 2020. Association for Computing Machinery.  ISBN 978-1-4503-7023-3.  doi: 10.1145/3366423.3380102.  URL http://doi.org/10.1145/3366423.3380102.
  * Yang et al. (2018a) Z. Yang, P. Qi, S. Zhang, Y. Bengio, W. Cohen, R. Salakhutdinov, and C. D. Manning.  Hotpotqa: A dataset for diverse, explainable multi-hop question answering.  In _Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing_ , pages 2369–2380, 2018a.
  * Yang et al. (2018b) Z. Yang, J. Zhao, B. Dhingra, K. He, W. W. Cohen, R. R. Salakhutdinov, and Y. LeCun.  Glomo: Unsupervised learning of transferable relational graphs.  In _Advances in Neural Information Processing Systems_ , pages 8950–8961, 2018b.
  * Yao et al. (2019a) L. Yao, C. Mao, and Y. Luo.  Graph convolutional networks for text classification.  In _The Thirty-Third AAAI Conference on Artificial Intelligence, AAAI 2019, The Thirty-First Innovative Applications of Artificial Intelligence Conference, IAAI 2019, The Ninth AAAI Symposium on Educational Advances in Artificial Intelligence, EAAI 2019, Honolulu, Hawaii, USA, January 27 - February 1, 2019_ , pages 7370–7377. AAAI Press, 2019a.
  * Yao et al. (2019b) L. Yao, C. Mao, and Y. Luo.  Graph convolutional networks for text classification.  In _Proc. AAAI Conf. Artif. Intell._ , volume 33, pages 7370–7377, Feb. 7-12, 2019b.
  * Yao et al. (2020) S. Yao, T. Wang, and X. Wan.  Heterogeneous graph transformer for graph-to-sequence learning.  In _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics_ , pages 7145–7154, 2020.
  * Yao et al. (2018) T. Yao, Y. Pan, Y. Li, and T. Mei.  Exploring visual relationship for image captioning.  In _Proceedings of the European conference on computer vision (ECCV)_ , pages 684–699, 2018.
  * Yasunaga et al. (2017) M. Yasunaga, R. Zhang, K. Meelu, A. Pareek, K. Srinivasan, and D. Radev.  Graph-based neural multi-document summarization.  In _Proceedings of the 21st Conference on Computational Natural Language Learning (CoNLL 2017)_ , pages 452–462, Vancouver, Canada, Aug. 2017\. Association for Computational Linguistics.  doi: 10.18653/v1/K17-1045.  URL https://www.aclweb.org/anthology/K17-1045.
  * Yasunaga et al. (2021) M. Yasunaga, H. Ren, A. Bosselut, P. Liang, and J. Leskovec.  Qa-gnn: Reasoning with language models and knowledge graphs for question answering.  2021\.
  * Ye et al. (2019) R. Ye, X. Li, Y. Fang, H. Zang, and M. Wang.  A vectorized relational graph convolutional network for multi-relational network alignment.  In _IJCAI_ , pages 4135–4141, 2019.
  * Yih et al. (2015) W.-t. Yih, M.-W. Chang, X. He, and J. Gao.  Semantic parsing via staged query graph generation: Question answering with knowledge base.  In _Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language Processing (Volume 1: Long Papers)_ , pages 1321–1331, 2015.
  * Yih et al. (2016) W.-t. Yih, M. Richardson, C. Meek, M.-W. Chang, and J. Suh.  The value of semantic parse labeling for knowledge base question answering.  In _Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers)_ , pages 201–206, 2016\.
  * Yin et al. (2018) P. Yin, G. Neubig, M. Allamanis, M. Brockschmidt, and A. L. Gaunt.  Learning to represent edits.  _arXiv preprint arXiv:1810.13337_ , 2018.
  * Yin et al. (2020) Y. Yin, F. Meng, J. Su, C. Zhou, Z. Yang, J. Zhou, and J. Luo.  A novel graph-based multi-modal fusion encoder for neural machine translation.  In _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics_ , pages 3025–3035, Online, July 2020. Association for Computational Linguistics.  doi: 10.18653/v1/2020.acl-main.273.  URL https://www.aclweb.org/anthology/2020.acl-main.273.
  * Ying et al. (2018) R. Ying, J. You, C. Morris, X. Ren, W. L. Hamilton, and J. Leskovec.  Hierarchical graph representation learning with differentiable pooling.  _arXiv preprint arXiv:1806.08804_ , 2018.
  * Yu et al. (2018) T. Yu, R. Zhang, K. Yang, M. Yasunaga, D. Wang, Z. Li, J. Ma, I. Li, Q. Yao, S. Roman, Z. Zhang, and D. Radev.  Spider: A large-scale human-labeled dataset for complex and cross-domain semantic parsing and text-to-SQL task.  In _Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing_ , pages 3911–3921, Brussels, Belgium, Oct.-Nov. 2018\. Association for Computational Linguistics.  doi: 10.18653/v1/D18-1425.  URL https://www.aclweb.org/anthology/D18-1425.
  * Yun et al. (2019) S. Yun, M. Jeong, R. Kim, J. Kang, and H. J. Kim.  Graph transformer networks.  _Advances in Neural Information Processing Systems_ , 32:11983–11993, 2019.
  * Zellers et al. (2018) R. Zellers, Y. Bisk, R. Schwartz, and Y. Choi.  Swag: A large-scale adversarial dataset for grounded commonsense inference.  _arXiv preprint arXiv:1808.05326_ , 2018.
  * Zeng et al. (2020) S. Zeng, R. Xu, B. Chang, and L. Li.  Double graph based reasoning for document-level relation extraction.  In _Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP)_ , pages 1630–1640, Online, Nov. 2020. Association for Computational Linguistics.  doi: 10.18653/v1/2020.emnlp-main.127.  URL https://www.aclweb.org/anthology/2020.emnlp-main.127.
  * Zhang et al. (2020a) B. Zhang, Y. Zhang, R. Wang, Z. Li, and M. Zhang.  Syntax-aware opinion role labeling with dependency graph convolutional networks.  In _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics_ , pages 3249–3258, 2020a.
  * Zhang et al. (2019a) C. Zhang, Q. Li, and D. Song.  Aspect-based Sentiment Classification with Aspect-specific Graph Convolutional Networks.  In _Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)_ , pages 4568–4578, Hong Kong, China, Nov. 2019a. Association for Computational Linguistics.  doi: 10.18653/v1/D19-1464.  URL https://www.aclweb.org/anthology/D19-1464.
  * Zhang et al. (2019b) C. Zhang, D. Song, C. Huang, A. Swami, and N. V. Chawla.  Heterogeneous graph neural network.  In _KDD_ , 2019b.
  * Zhang et al. (2019c) C. Zhang, D. Song, C. Huang, A. Swami, and N. V. Chawla.  Heterogeneous graph neural network.  In _Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining_, pages 793–803, 2019c.
  * Zhang et al. (2020b) J. Zhang, L. Wang, R. K.-W. Lee, Y. Bin, Y. Wang, J. Shao, and E.-P. Lim.  Graph-to-tree learning for solving math word problems.  In _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics_ , pages 3928–3937, Online, July 2020b. Association for Computational Linguistics.  doi: 10.18653/v1/2020.acl-main.362.  URL https://www.aclweb.org/anthology/2020.acl-main.362.
  * Zhang and Qian (2020) M. Zhang and T. Qian.  Convolution over hierarchical syntactic and lexical graphs for aspect level sentiment analysis.  In _Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP)_ , pages 3540–3549, Online, Nov. 2020. Association for Computational Linguistics.  doi: 10.18653/v1/2020.emnlp-main.286.  URL https://www.aclweb.org/anthology/2020.emnlp-main.286.
  * Zhang et al. (2019d) N. Zhang, S. Deng, Z. Sun, G. Wang, X. Chen, W. Zhang, and H. Chen.  Long-tail relation extraction via knowledge graph embeddings and graph convolution networks.  In _Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers)_ , pages 3016–3025, Minneapolis, Minnesota, June 2019d. Association for Computational Linguistics.  doi: 10.18653/v1/N19-1306.  URL https://www.aclweb.org/anthology/N19-1306.
  * Zhang et al. (2020c) N. Zhang, S. Deng, J. Li, X. Chen, W. Zhang, and H. Chen.  Summarizing Chinese medical answer with graph convolution networks and question-focused dual attention.  In _Findings of the Association for Computational Linguistics: EMNLP 2020_ , pages 15–24, Online, Nov. 2020c. Association for Computational Linguistics.  doi: 10.18653/v1/2020.findings-emnlp.2.  URL https://www.aclweb.org/anthology/2020.findings-emnlp.2.
  * Zhang et al. (2018a) S. Zhang, X. Liu, J. Liu, J. Gao, K. Duh, and B. Van Durme.  Record: Bridging the gap between human and machine commonsense reading comprehension.  _arXiv preprint arXiv:1810.12885_ , 2018a.
  * Zhang et al. (2019e) S. Zhang, X. Ma, K. Duh, and B. Van Durme.  AMR parsing as sequence-to-graph transduction.  In _Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics_ , pages 80–94, Florence, Italy, July 2019e. Association for Computational Linguistics.  doi: 10.18653/v1/P19-1009.  URL https://www.aclweb.org/anthology/P19-1009.
  * Zhang et al. (2015) X. Zhang, J. Zhao, and Y. LeCun.  Character-level convolutional networks for text classification.  _arXiv preprint arXiv:1509.01626_ , 2015.
  * Zhang et al. (2017a) Y. Zhang, W. Chan, and N. Jaitly.  Very deep convolutional networks for end-to-end speech recognition.  In _2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)_ , pages 4845–4849. IEEE, 2017a.
  * Zhang et al. (2017b) Y. Zhang, V. Zhong, D. Chen, G. Angeli, and C. D. Manning.  Position-aware attention and supervised data improve slot filling.  In _Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing_ , pages 35–45, 2017b.
  * Zhang et al. (2018b) Y. Zhang, H. Dai, Z. Kozareva, A. Smola, and L. Song.  Variational reasoning for question answering with knowledge graph.  In _Proceedings of the AAAI Conference on Artificial Intelligence_ , volume 32, 2018b.
  * Zhang et al. (2018c) Y. Zhang, Q. Liu, and L. Song.  Sentence-state lstm for text representation.  In _Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pages 317–327, 2018c.
  * Zhang et al. (2018d) Y. Zhang, P. Qi, and C. D. Manning.  Graph convolution over pruned dependency trees improves relation extraction.  In _Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing_ , pages 2205–2215, Brussels, Belgium, Oct.-Nov. 2018d. Association for Computational Linguistics.  doi: 10.18653/v1/D18-1244.  URL https://www.aclweb.org/anthology/D18-1244.
  * Zhang et al. (2020d) Y. Zhang, Z. Guo, Z. Teng, W. Lu, S. B. Cohen, Z. Liu, and L. Bing.  Lightweight, dynamic graph convolutional networks for AMR-to-text generation.  In _Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP)_ , pages 2162–2172, Online, Nov. 2020d. Association for Computational Linguistics.  doi: 10.18653/v1/2020.emnlp-main.169.  URL https://www.aclweb.org/anthology/2020.emnlp-main.169.
  * Zhang et al. (2020e) Y. Zhang, X. Yu, Z. Cui, S. Wu, Z. Wen, and L. Wang.  Every document owns its structure: Inductive text classification via graph neural networks.  In D. Jurafsky, J. Chai, N. Schluter, and J. R. Tetreault, editors, _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, ACL 2020, Online, July 5-10, 2020_ , pages 334–339. Association for Computational Linguistics, 2020e.
  * Zhang et al. (2020f) Y. Zhang, X. Yu, Z. Cui, S. Wu, Z. Wen, and L. Wang.  Every document owns its structure: Inductive text classification via graph neural networks.  _arXiv preprint arXiv:2004.13826_ , 2020f.
  * Zhang et al. (2020g) Z. Zhang, F. Zhuang, H. Zhu, Z.-P. Shi, H. Xiong, and Q. He.  Relational graph neural network with hierarchical attention for knowledge graph completion.  In _AAAI_ , pages 9612–9619, 2020g.
  * Zhao et al. (2021) J. Zhao, X. Wang, C. Shi, B. Hu, G. Song, and Y. Ye.  Heterogeneous graph structure learning for graph neural networks.  In _Proceedings of the AAAI Conference on Artificial Intelligence_ , 2021.
  * Zhao et al. (2020a) L. Zhao, W. Xu, and J. Guo.  Improving abstractive dialogue summarization with graph structures and topic words.  In _Proceedings of the 28th International Conference on Computational Linguistics_ , pages 437–449, Barcelona, Spain (Online), Dec. 2020a. International Committee on Computational Linguistics.  URL https://www.aclweb.org/anthology/2020.coling-main.39.
  * Zhao et al. (2020b) Y. Zhao, L. Chen, Z. Chen, R. Cao, S. Zhu, and K. Yu.  Line graph enhanced AMR-to-text generation with mix-order graph attention networks.  In _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics_ , pages 732–741, Online, July 2020b. Association for Computational Linguistics.  doi: 10.18653/v1/2020.acl-main.67.  URL https://www.aclweb.org/anthology/2020.acl-main.67.
  * Zhao et al. (2020c) Y. Zhao, L. Xiang, J. Zhu, J. Zhang, Y. Zhou, and C. Zong.  Knowledge graph enhanced neural machine translation via multi-task learning on sub-entity granularity.  In _Proceedings of the 28th International Conference on Computational Linguistics_ , pages 4495–4505, Barcelona, Spain (Online), Dec. 2020c. International Committee on Computational Linguistics.  URL https://www.aclweb.org/anthology/2020.coling-main.397.
  * Zheng et al. (2020) B. Zheng, H. Wen, Y. Liang, N. Duan, W. Che, D. Jiang, M. Zhou, and T. Liu.  Document modeling with graph attention networks for multi-grained machine reading comprehension.  In D. Jurafsky, J. Chai, N. Schluter, and J. R. Tetreault, editors, _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, ACL 2020, Online, July 5-10, 2020_ , pages 6708–6718. Association for Computational Linguistics, 2020.
  * Zheng and Kordjamshidi (2020) C. Zheng and P. Kordjamshidi.  Srlgrn: Semantic role labeling graph reasoning network.  In _Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP)_ , pages 8881–8891, 2020.
  * Zhong et al. (2017) V. Zhong, C. Xiong, and R. Socher.  Seq2sql: Generating structured queries from natural language using reinforcement learning.  _arXiv preprint arXiv:1709.00103_ , 2017.
  * Zhou et al. (2020a) D. Zhou, X. Hu, and R. Wang.  Neural Topic Modeling by Incorporating Document Relationship Graph.  In _Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP)_ , pages 3790–3796, Online, Nov. 2020a. Association for Computational Linguistics.  doi: 10.18653/v1/2020.emnlp-main.310.  URL https://www.aclweb.org/anthology/2020.emnlp-main.310.
  * Zhou et al. (2018a) H. Zhou, T. Young, M. Huang, H. Zhao, J. Xu, and X. Zhu.  Commonsense knowledge aware conversation generation with graph attention.  In _IJCAI_ , pages 4623–4629, 2018a.
  * Zhou et al. (2018b) Q. Zhou, N. Yang, F. Wei, S. Huang, M. Zhou, and T. Zhao.  Neural document summarization by jointly learning to score and select sentences.  _arXiv preprint arXiv:1807.02305_ , 2018b.
  * Zhou et al. (2020b) Q. Zhou, Y. Zhang, D. Ji, and H. Tang.  AMR parsing with latent structural information.  In _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics_ , pages 4306–4319, Online, July 2020b. Association for Computational Linguistics.  doi: 10.18653/v1/2020.acl-main.397.  URL https://www.aclweb.org/anthology/2020.acl-main.397.
  * Zhu et al. (2019a) H. Zhu, Y. Lin, Z. Liu, J. Fu, T.-S. Chua, and M. Sun.  Graph neural networks with generated parameters for relation extraction.  In _Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics_ , pages 1331–1339, Florence, Italy, July 2019a. Association for Computational Linguistics.  doi: 10.18653/v1/P19-1128.  URL https://www.aclweb.org/anthology/P19-1128.
  * Zhu et al. (2019b) J. Zhu, J. Li, M. Zhu, L. Qian, M. Zhang, and G. Zhou.  Modeling graph structure in transformer for better AMR-to-text generation.  In _Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)_ , pages 5459–5468, Hong Kong, China, Nov. 2019b. Association for Computational Linguistics.  doi: 10.18653/v1/D19-1548.  URL https://www.aclweb.org/anthology/D19-1548.
  * Zhu et al. (2019c) J. Zhu, J. Li, M. Zhu, L. Qian, M. Zhang, and G. Zhou.  Modeling graph structure in transformer for better amr-to-text generation.  In _Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing_ , pages 5458–5467. Association for Computational Linguistics, 2019c.
  * Zhu et al. (2018) Q. Zhu, Z. Feng, and X. Li.  GraphBTM: Graph Enhanced Autoencoded Variational Inference for Biterm Topic Model.  In _Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing_ , pages 4663–4672, Brussels, Belgium, Oct. 2018. Association for Computational Linguistics.  doi: 10.18653/v1/D18-1495.  URL https://www.aclweb.org/anthology/D18-1495.


# Differential Phase Shift Quantum Secret Sharing Using a Twin Field with
Asymmetric Source Intensities

Zhao-Ying Jia  Jie Gu  Bing-Hong Li  Hua-Lei Yin<EMAIL_ADDRESS>Zeng-Bing
Chen<EMAIL_ADDRESS>National Laboratory of Solid State Microstructures,
School of Physics, and Collaborative Innovation Center of Advanced
Microstructures, Nanjing University, Nanjing 210093, China

###### Abstract

As an essential application of quantum mechanics in classical cryptography,
quantum secret sharing has become an indispensable component of quantum
internet. Recently, a differential phase shift quantum secret sharing protocol
using a twin field has been proposed to break the linear rate-distance
boundary. However, this original protocol has a poor performance over channels
with asymmetric transmittances. To make it more practical, we present a
differential phase shift quantum secret sharing protocol with asymmetric
source intensities and give the security proof of our protocol against
individual attacks. Taking finite-key effects into account, our asymmetric
protocol can theoretically obtain the key rate two orders of magnitude higher
than that of the original protocol when the difference in length between
Alice’s channel and Bob’s is fixed at 14 km. Moreover, our protocol can
provide a high key rate even when the difference is quite large and has great
robustness against finite-key effects. Therefore, our work is meaningful for
the real-life applications of quantum secret sharing.

##  I INTRODUCTION

Secret sharing is a cryptographic protocol in which a dealer splits a secret
into several parts and distributes them among various players. The secret can
be recovered only when a sufficient number of players (authorized subsets)
cooperate to share their parts of the secret. The classical secret sharing
scheme was first introduced independently by Shamir [1] and Blakley [2] in
1979, followed by plenty of variations [3]. However, all existing classical
secret sharing schemes are not perfectly secure from eavesdropping attacks
[4].

As the combination of classical secret sharing and quantum mechanics, quantum
secret sharing (QSS) is more secure due to the excellent properties of quantum
theory and has become one of the most attractive research topics in the
quantum cryptography. In 1999, Hillery et al. [5] firstly proposed a protocol
of QSS using a three-photon Greenberger–Horne–Zeilinger (GHZ) state.
Afterwards, this protocol was generalized into an arbitrary number of parties
based on multi-particle entanglement states [6], and later to multi-particle
$d$-dimensional entanglement states [7]. From then on, much theoretical [8, 9,
10, 11, 12, 13, 14, 15] and experimental [16, 17, 18, 19] attention has
focused on QSS using multi-particle entangled states. However, it is a
tremendous challenge to prepare a multiparty entanglement state with high
fidelity and efficiency, which makes particle entanglement-based QSS
unscalable. To circumvent the problems, differential phase shift QSS scheme
using coherent light [20], similar to those used in quantum key distribution
(QKD) [21, 22, 23, 24, 25, 26], has been proposed and implemented.

Nevertheless, the linear rate-distance limitation constricts the key rate and
transmission distance of QSS [27, 28]. Recently, to exceed the linear bound
and further enhance the practical performance of QSS, a differential phase
shift quantum secret sharing (DPSQSS) protocol [29] using a twin field (TF)
[30] has been proposed. Unfortunately, this protocol suffers from low key rate
and short transmission distance over channels with different transmittances,
which constrains its application in a practical network setting.

Here, we propose an asymmetric differential phase shift quantum secret sharing
protocol using twin field [30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42,
43, 44] ideas and give the security proof of this protocol against individual
attacks. The key point of our method is that Alice and Bob can adjust their
source intensities independently to effectively compensate for channel
asymmetry. The numerical results show that our protocol is robust against
finite-key effects [45, 46, 47, 48] and can theoretically provide a two orders
of magnitude higher key rate than the original protocol with the length
difference between Alice’s channel and Bob’s fixed at 14 km. Furthermore, our
protocol still obtains a high key rate when the difference in length is fixed
at 50,100 km, whereas no keys are obtained with the same difference in the
original protocol. Therefore, our work represents a further step along the
progress of practical QSS.

##  II TF-DPSQSS Protocol with Asymmetric Source Intensities

The schematic diagram of our asymmetric protocol is shown in Fig. 1, where
Alice and Bob have partial keys for deciphering, and Charlie has a full key
for ciphering. The two senders, Alice and Bob, independently prepare two
trains of weak coherent pulses whose intensities are different and phases are
randomly modulated to be 0 or $\pi$. The coherent pulses are sent through the
quantum channels and received by the trusted third party, Charlie, who
measures them using an unbalanced interferometer. The details of the protocol
are shown as follows.

Figure 1: Configuration of our quantum secret sharing protocol. Weak coherent
pulse sources (Laser); phase modulator (PM); signal attenuator (Att);
transmittance of channels between Alice (Bob) and Charlie
($\eta_{a},\eta_{b}$); polarization control (PC); beam splitter (BS); single
photon detector (D1, D2). In Charlie’s measurement area, two pulse trains are
first polarization-modulated by polarization controls to correct their
polarization for interference. Then, Charlie divides each incoming pulse into
two paths and recombines them by a 50:50 beam splitter, where the path-length
difference is set equal to the time T. Detectors are placed at the two outputs
of the recombining beam splitter. At the detectors, the partial wave functions
of two senders’ pulses that are in the same time slots interfere with each
other.

Preparation: Alice (Bob) prepares a weak coherent pulse train and phase-
modulates each pulse randomly by 0 or $\pi$. The coherent states can be
denoted as
$\left|\psi_{a}\right\rangle=\underset{n=1}{\overset{N}{\otimes}}\left|\sqrt{\mu_{a}}e^{i{\phi_{n}^{a}}}\right\rangle$
$\left(|\psi_{b}\right\rangle=\underset{n=1}{\overset{N}{\otimes}}\left|\sqrt{\mu_{b}}e^{i{\phi_{n}^{b}}}\right\rangle)$.
Then, she (he) sends out the coherent state pulse whose period is 2T to
Charlie with an average photon number less than one per pulse. Alice (Bob)
records her (his) logic bits of each time slot as “0” (“1”) when her (his)
modulated phase is 0 $(\pi)$. We denote the sequence of detection events time
slots as $n$ $\in\left\\{1,2,3,...,2N\right\\}$, where $N$ is the total number
of pulses sent by Alice (Bob). The phase shift
$\phi_{n}^{a}\left(\phi_{n}^{b}\right)\in\left\\{0,\pi\right\\}$ is the phase
induced by the phase modulator on pulse $n$ ignoring the global phase, and
intensities $\mu_{a}$, $\mu_{b}$ are corresponding to Alice and Bob,
respectively.

Measurement: As illustrated in Fig. 1, while measuring the signal, Charlie
records the photon detection time and which detector clicks. When the
detection event time slots are corresponding to the time $2kT$, detector 1
will click for 0 phase difference between the two senders’ pulses and detector
2 will click for $\pi$ phase difference. When the detection event time slots
are corresponding to the time $(2k+1)T$, detector 1 will click for $\pi$ phase
difference and detector 2 will click for 0 phase difference. Note that if both
detectors click, Charlie randomly chooses one detector click to record. Here,
a photon is detected occasionally and randomly because the received signal
power is smaller than one photon per pulse.

Using the above setup, Charlie creates his key shown in Table. 1 . “0” means
that the modulated phases in one time slot imposed by Alice and Bob are
$\left\\{0,0\right\\}$ or $\left\\{\pi,\pi\right\\}$, and“1” means that the
modulated phases in one time slot imposed by Alice and Bob are
$\left\\{0,\pi\right\\}$ or $\left\\{\pi,0\right\\}$. Thus, Charlie’s bits are
exclusive OR of Alice’s and Bob’s bits. That is, Alice and Bob know Charlie’s
key bits only when they cooperate, and the QSS operation is accomplished.

Table 1: Logic bits held by Charlie corresponding to different detection event time slots when detector 1 or detector 2 clicks. | Detector$1$ | Detector$2$
---|---|---
$2kT$ | “0” | “1”
$(2k+1)T$ | “1” | “0”

Parameter estimation: Charlie randomly chooses recorded detection times and
Alice and Bob alternatively disclose her or their test bit first in the chosen
time slots through a public channel. Then, Charlie will get the quantum bit
error rate (QBER) and make a decision whether they discard all their bits and
restart the whole QSS at Step 1 (preparation).

Postprocessing: After calculating the QBER, Alice, Bob, and Charlie will
conduct classical error correction and privacy amplification to distill the
final full key and partial keys.

##  III Proof of Security

In this section, we will discuss the security of our protocol against
eavesdropping. Because of the equivalence [29] between our asymmetric protocol
and differential phase shift QSS, we can apply the conclusion in differential
phase shift quantum key distribution [25] to the analysis of both an external
eavesdropper and an internal eavesdropper in our protocol.

###  III.1 External Eavesdropping

Firstly, Eve cannot obtain full key information by beam-splitting attacks and
intercept-resend attacks, which will result in bit errors in the secret key
[22]. As for a general individual attack, based on the assumption that Eve
will conduct the same attack in differential phase shift QSS [20], we can
derive that information leakage to Eve is given by a fraction
$\mu_{a}(1-\eta_{a})+\mu_{b}(1-\eta_{b})$ of the sifted key [25].

###  III.2 Internal Eavesdropping

QSS protocols have to prohibit Alice or Bob from knowing Charlie’s key by
herself or himself. Firstly, we assume that Bob is the malicious one. In this
case, we have equivalence configuration [29] shown in Fig. 2a. Bob wants to
know Charlie’s key by himself, and also needs to know Alice’s modulation phase
to pass the test-bit checking among Alice, Bob, and Charlie after the creation
of the raw key. A configuration for Bob to do so is shown in Fig. 2b. He
conducts general individual attacks as carried out by Eve in differential
phase shift quantum key distribution [25], where the fraction Bob obtains
about Charlie’s bits is $2\mu_{a}$. Similarly, when Alice is the malicious
one, the probability that Alice knows Bob’s differential phase corresponding
to Charlie’s bit is $2\mu_{b}$. From the above discussion, we denote
$\mu_{\max}=\max\left\\{\mu_{a},\mu_{b}\right\\}$ as the maximum intensity,
then $2\mu_{\max}$ is the maximum ratio of information that a malicious one
can obtain from the internal eavesdropping.

Figure 2:  Internal eavesdropping of malicious Bob. (a) With some special
rules discussed in [29], we present the configuration of equivalence between
differential phase shift QSS and our protocol. (b) We present the
configuration of a general individual attack by malicious Bob.

In conclusion, we find that the probability information leakage to Eve and
malicious Bob (Alice) is $\mu_{a}(1-\eta_{a})+\mu_{b}(1-\eta_{b})$ and
$2\mu_{a}{(2\mu_{b})}$. We discover that information leakage to external Eve
is slightly lower than that to malicious Bob (Alice). For simplicity, we can
just consider information leakage in our protocol to be $2\mu_{\max}$.

##  IV Numerical Simulation

###  IV.1 Mathematical Calculation with Asymmetric Channels

Based on the asymmetric protocol description, Charlie generates their
classical bits according to the phase differences between Alice and Bob in the
same time slot. To obtain the secure key rate, we apply the same denotations
in previous sections that Alice and Bob send pulses with intensities
$\mu_{a}$, $\mu_{b}$, and the distance between Alice (Bob) and Charlie is
$l_{a}(l_{b})$. In our scheme, the channel transmittance between Alice (Bob)
and Charlie is $\eta_{a}=\eta_{d}\times 10^{-{\alpha
l_{a}}/{10}}(\eta_{b}=\eta_{d}\times 10^{-{\alpha l_{b}}/{10}})$, where
$\eta_{d}$ is the detection efficiency of Charlie’s detectors and $\alpha$ is
the attenuation coefficient of the ultra-low fiber. In addition, let us
suppose that $p_{d}$ is the dark count rate of one detector. For two detectors
used by Charlie, we derive the total dark count rate as $2p_{d}$ and the error
rate of background $e_{0}=\frac{1}{2}$.

In Charlie’s laboratory, after the BS (see Figure 1), the optical intensities
received by detector 1 and detector 2 are given by
$D_{1}=(\frac{\sqrt{\mu_{a}\eta_{a}}}{2}+\frac{\sqrt{\mu_{b}\eta_{b}}}{2}\cos{\theta})^{2}$
and
$D_{2}=(\frac{\sqrt{\mu_{a}\eta_{a}}}{2}-\frac{\sqrt{\mu_{b}\eta_{b}}}{2}\cos{\theta})^{2}$,
where $\theta$ denotes the relative phase between Alice’s and Bob’s weak
coherent states. In our asymmetric protocol, we have
$\theta\in\left\\{0,\pi\right\\}$. Thus, the detection probability of each
detector is: $Q_{1}=1-(1-p_{d})e^{-D_{1}}$, $Q_{2}=1-(1-p_{d})e^{-D_{2}}$.

The gain of the whole system for Charlie’s detections can be calculated by
$Q_{\mu}=Q_{1}(1-Q_{2})+Q_{2}(1-Q_{1})+Q_{1}Q_{2}$ and the error rate of the
total gain can be derived by
$E_{\mu}Q_{\mu}=e_{d}Q_{1}(1-Q_{2})+(1-e_{d})Q_{2}(1-Q_{1})+\frac{1}{2}Q_{1}Q_{2}$,
where $e_{d}$ is the misalignment error rate of detectors.

###  IV.2 Finite-Key Analysis Method for Our Protocol

Considering the finite-key effects, let $n_{\mu}=NQ_{\mu}$ be the observed
number of bits, where $N$ is the number of optical pulses sent by Alice and
Bob. By using the random sampling without replacement [47], one can calculate
the upper bound of hypothetically observed error rate associated with
$E_{\mu}$ with a failure probability $\epsilon_{RS}$:

$\overline{E_{\mu}}=E_{\mu}+\gamma(n_{\mu}-k,k,E_{\mu},\epsilon_{RS}),$ (1)

where $k$ is the number of bits in the chosen time slots at Step 3 (parameter
estimation).

In the following, we assume the protocol is $\epsilon$-secure [49] where the
maximum failure probability of practical protocol is $\epsilon$. According to
universally composable security [50],

$\epsilon=\epsilon_{RS}+\overline{\epsilon}+\epsilon_{EC}+\epsilon_{PA},$ (2)

where $\overline{\epsilon}$ represents the accuracy of estimating the smooth
min-entropy. In addition, $\epsilon_{EC}$ corresponds to the probability that
error correction fails and $\epsilon_{PA}$ is the probability that privacy
amplification fails.

Then we obtain the key rate formula in finite-sized key region, which reads

$\displaystyle R_{\rm QSS}=$ $\displaystyle
Q_{\mu}[-(1-2\mu_{\max})\log_{2}(P_{\rm co})-f_{e}h(E_{\mu})]$ (3)
$\displaystyle-\dfrac{7}{N}\sqrt{n_{\mu}\log_{2}{\dfrac{2}{\overline{\epsilon}}}}-\dfrac{1}{N}\log_{2}{\dfrac{2}{\epsilon_{EC}}}-\dfrac{2}{N}\log_{2}{\dfrac{1}{\epsilon_{PA}}}.$

Here, $f_{e}$ is the error correction efficiency and
$h(x)=-x\log_{2}(x)-(1-x)\log_{2}(1-x)$ is Shannon entropy. $P_{\rm co}$ is
the upper bound of collision probability when considering individual attacks,
which can be concluded as $P_{\rm
co}=1-\overline{E_{\mu}}^{2}-{(1-6\overline{E_{\mu}})^{2}}/{2}$ [51].

###  IV.3 Results of Simulation

We use the genetic algorithm to run the numerical simulations, and the key
rate is optimized over the free parameters. Here, we set
$\epsilon_{RS}=\overline{\epsilon}=\epsilon_{EC}=\epsilon_{PA}=10^{-10}$ and
utilize experimental parameters listed in Table. 2. Fig. 3 shows how the key
rate varies with transmission distance between Alice and Bob when their
channels have the same transmittance, where the total pulses are set as
$N=10^{12},N=10^{10},N=10^{8}$, respectively. We can find that our protocol
shows great robustness against finite-key effects. In Fig. 4, we plot the
results of our asymmetric protocol when the total pulses are set $N=10^{12}$,
where the difference in length between Alice’s channel and Bob’s is fixed at
10 km, 50 km, and 100 km, respectively.

Figure 3: The performance of our protocol under symmetric channels. Under the
experimental parameters listed in Table. 2, we simulate results in the case
that $l_{a}=l_{b}$, where $N=10^{12},$ $N=10^{10}$, and $N=10^{8}$. Figure 4:
The performance of our protocol under asymmetric channels. Under the
experimental parameters listed in Table. 2, we simulate results in the case
that $N=10^{12}$, where $l_{b}-l_{a}=10,50,100$ km.

When the original TF-DPSQSS [29] protocol is applied to the asymmetric
channels, a high system error rate will arise since different channel
transmittances will lead to the poor performance of interference at the beam
splitter. Fig. 5 presents numerical results of our asymmetric protocols and
the original TF-DPSQSS [29] protocol with the difference in length between two
channels fixed at $10$ km and $14$ km. We can see clearly from Fig. 5 that our
asymmetric protocol improves the secret key rate by two orders of magnitude
when $l_{b}-l_{a}=14$ km. Moreover, no keys are obtained with difference fixed
at 50, 100 km in the original protocol, whereas Fig. 4 shows that our protocol
still provides a high key rate when the difference is large. It means that in
the asymmetric channels, the performance of the asymmetric protocol is much
better than that of the original protocol, especially when channels are
extremely asymmetric.

Figure 5: Quantum secret sharing key rate vs transmission distance between Alice and Bob. Under the experimental parameters listed in Table. 2, we compare the simulation results of the original TF-DPSQSS [29] protocol and our asymmetric protocol with $N=10^{12}$, where the difference in length between Alice’s and Bob’s channels is fixed at 10 km, 14 km. Table 2: Simulation parameters. $\eta_{d}$ and $p_{d}$ are the detection efficiency and dark count rate. $\alpha$ is the attenuation coefficient of the ultra-low fiber. $f_{e}$ is the error correction efficiency. $\eta_{d}$ | $p_{d}$ | $\alpha$ | $f_{e}$
---|---|---|---
$55\%$ | $10^{-8}$ | $0.165$ | $1.15$

##  V Conclusion

In summary, we propose a differential phase shift quantum secret sharing
protocol over asymmetric channels and give the security proof of our protocol
against individual attacks. Moreover, we extend the asymptotic key rate of TF-
DPSQSS [29] to finite-key region. Through implementing free parameter
optimization on the numerical simulations, we demonstrate that our asymmetric
protocol can dramatically improve the key generation rate and the transmission
distance compared with the original TF-DPSQSS [29] protocol. As we have shown
before, when the difference in length between Alice’s channel and Bob’s is
fixed at 14 km, the key rate of the asymmetric protocol is two orders of
magnitude higher than the original TF-DPSQSS [29] protocol. Furthermore, our
protocol obtains a high key rate when the difference is large. In addition, it
is convenient and efficient to implement by allowing Alice and Bob to set
asymmetric intensities independently, especially in a network setting. Due to
the remarkable performance of our asymmetric protocol, it can be applied
directly to the QSS experiments over asymmetric channels and represents a
further step towards practical application of QSS.

## Acknowledgments

We acknowledge support from the National Natural Science Foundation of China
(61801420); Key-Area Research and Development Program of Guangdong Province
(2020B0303040001); Fundamental Research Funds for the Central Universities
(020414380182, 020414380141).

## References

  * Shamir [1979] A. Shamir, How to share a secret, Commun. ACM 22, 612 (1979).
  * Blakley [1979] G. R. Blakley, Safeguarding cryptographic keys, in In Proceedings of the 1979 AFIPS National Computer Conference, Vol. 48 (New York, NY, USA, 1979) pp. 313–317.
  * Brickell [1989] E. F. Brickell, Some ideal secret sharing schemes, in Workshop on the Theory and Application of of Cryptographic Techniques (Springer, 1989) pp. 468–475.
  * Shor [1994] P. Shor, Algorithms for quantum computation: discrete logarithms and factoring, in Proceedings 35th Annual Symposium on Foundations of Computer Science (1994) pp. 124–134.
  * Hillery et al. [1999] M. Hillery, V. Bužek, and A. Berthiaume, Quantum secret sharing, Phys. Rev. A 59, 1829 (1999).
  * Xiao et al. [2004] L. Xiao, G. L. Long, F.-G. Deng, and J.-W. Pan, Efficient multiparty quantum-secret-sharing schemes, Phys. Rev. A 69, 052307 (2004).
  * Yu et al. [2008] I.-C. Yu, F.-L. Lin, and C.-Y. Huang, Quantum secret sharing with multilevel mutually (un) biased bases, Phys. Rev. A 78, 012344 (2008).
  * Nascimento et al. [2001] A. C. A. Nascimento, J. Mueller-Quade, and H. Imai, Improving quantum secret-sharing schemes, Phys. Rev. A 64, 042311 (2001).
  * Singh and Srikanth [2005] S. K. Singh and R. Srikanth, Generalized quantum secret sharing, Phys. Rev. A 71, 012328 (2005).
  * Keet et al. [2010] A. Keet, B. Fortescue, D. Markham, and B. C. Sanders, Quantum secret sharing with qudit graph states, Phys. Rev. A 82, 062315 (2010).
  * Fu et al. [2015] Y. Fu, H.-L. Yin, T.-Y. Chen, and Z.-B. Chen, Long-distance measurement-device-independent multiparty quantum communication, Phys. Rev. Lett. 114, 090501 (2015).
  * Rahaman and Parker [2015] R. Rahaman and M. G. Parker, Quantum scheme for secret sharing based on local distinguishability, Phys. Rev. A 91, 022330 (2015).
  * Tavakoli et al. [2015] A. Tavakoli, I. Herbauts, M. Żukowski, and M. Bourennane, Secret sharing with a single $d$-level quantum system, Phys. Rev. A 92, 030302 (2015).
  * Kogias et al. [2017] I. Kogias, Y. Xiang, Q. He, and G. Adesso, Unconditional security of entanglement-based continuous-variable quantum secret sharing, Phys. Rev. A 95, 012315 (2017).
  * Qin et al. [2020] H. Qin, W. K. S. Tang, and R. Tso, Hierarchical quantum secret sharing based on special high-dimensional entangled state, IEEE J. Sel. Top. Quantum Electron 26, 6600106 (2020).
  * Tittel et al. [2001] W. Tittel, H. Zbinden, and N. Gisin, Experimental demonstration of quantum secret sharing, Phys. Rev. A 63, 042301 (2001).
  * Chen et al. [2005] Y.-A. Chen, A.-N. Zhang, Z. Zhao, X.-Q. Zhou, C.-Y. Lu, C.-Z. Peng, T. Yang, and J.-W. Pan, Experimental quantum secret sharing and third-man quantum cryptography, Phys. Rev. Lett. 95, 200502 (2005).
  * Gaertner et al. [2007] S. Gaertner, C. Kurtsiefer, M. Bourennane, and H. Weinfurter, Experimental demonstration of four-party quantum secret sharing, Phys. Rev. Lett. 98, 020503 (2007).
  * Bell et al. [2014] B. Bell, D. Markham, D. Herrera-Martí, A. Marin, W. Wadsworth, J. Rarity, and M. Tame, Experimental demonstration of graph-state quantum secret sharing, Nat. Commun. 5, 5480 (2014).
  * Inoue et al. [2008] K. Inoue, T. Ohashi, T. Kukita, K. Watanabe, S. Hayashi, T. Honjo, and H. Takesue, Differential-phase-shift quantum secret sharing, Opt. Express 16, 15469 (2008).
  * Inoue et al. [2002] K. Inoue, E. Waks, and Y. Yamamoto, Differential phase shift quantum key distribution, Phys. Rev. Lett. 89, 037902 (2002).
  * Inoue et al. [2003] K. Inoue, E. Waks, and Y. Yamamoto, Differential-phase-shift quantum key distribution using coherent light, Phys. Rev. A 68, 022317 (2003).
  * Honjo et al. [2004] T. Honjo, K. Inoue, and H. Takahashi, Differential-phase-shift quantum key distribution experiment with a planar light-wave circuit mach–zehnder interferometer, Opt. Lett. 29, 2797 (2004).
  * Takesue et al. [2005] H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, Differential phase shift quantum key distribution experiment over 105 km fibre, New J. Phys. 7, 232 (2005).
  * Waks et al. [2006] E. Waks, H. Takesue, and Y. Yamamoto, Security of differential-phase-shift quantum key distribution against individual attacks, Phys. Rev. A 73, 012344 (2006).
  * Diamanti et al. [2006] E. Diamanti, H. Takesue, C. Langrock, M. M. Fejer, and Y. Yamamoto, 100 km differential phase shift quantum key distribution experiment with low jitter up-conversion detectors, Opt. Express 14, 13073 (2006).
  * Takeoka et al. [2014] M. Takeoka, S. Guha, and M. M. Wilde, Fundamental rate-loss tradeoff for optical quantum key distribution, Nat. Commun. 5, 5235 (2014).
  * Pirandola et al. [2017] S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi, Fundamental limits of repeaterless quantum communications, Nat. Commun. 8, 15043 (2017).
  * Gu et al. [2021] J. Gu, X.-Y. Cao, H.-L. Yin, and Z.-B. Chen, Differential phase shift quantum secret sharing using a twin field, Opt. Express 29, 9165 (2021).
  * Lucamarini et al. [2018] M. Lucamarini, Z. L. Yuan, J. F. Dynes, and A. J. Shields, Overcoming the rate–distance limit of quantum key distribution without quantum repeaters, Nature 557, 400 (2018).
  * Ma et al. [2018] X. Ma, P. Zeng, and H. Zhou, Phase-matching quantum key distribution, Phys. Rev. X 8, 031043 (2018).
  * Wang et al. [2018] X.-B. Wang, Z.-W. Yu, and X.-L. Hu, Twin-field quantum key distribution with large misalignment error, Phys. Rev. A 98, 062323 (2018).
  * Lin and Lütkenhaus [2018] J. Lin and N. Lütkenhaus, Simple security analysis of phase-matching measurement-device-independent quantum key distribution, Phys. Rev. A 98, 042332 (2018).
  * Yin and Fu [2019] H.-L. Yin and Y. Fu, Measurement-device-independent twin-field quantum key distribution, Sci. Rep. 9, 3045 (2019).
  * Cui et al. [2019] C. Cui, Z.-Q. Yin, R. Wang, W. Chen, S. Wang, G.-C. Guo, and Z.-F. Han, Twin-field quantum key distribution without phase postselection, Phys. Rev. Applied 11, 034053 (2019).
  * Curty et al. [2019] M. Curty, K. Azuma, and H.-K. Lo, Simple security proof of twin-field type quantum key distribution protocol, npj Quantum Inf. 5, 64 (2019).
  * Yin and Chen [2019a] H.-L. Yin and Z.-B. Chen, Coherent-state-based twin-field quantum key distribution, Sci. Rep. 9, 14918 (2019a).
  * Hu et al. [2019] X.-L. Hu, C. Jiang, Z.-W. Yu, and X.-B. Wang, Sending-or-not-sending twin-field protocol for quantum key distribution with asymmetric source parameters, Phys. Rev. A 100, 062337 (2019).
  * Grasselli et al. [2019] F. Grasselli, Á. Navarrete, and M. Curty, Asymmetric twin-field quantum key distribution, New J. Phys. 21, 113032 (2019).
  * Maeda et al. [2019] K. Maeda, T. Sasaki, and M. Koashi, Repeaterless quantum key distribution with efficient finite-key analysis overcoming the rate-distance limit, Nat. Commun. 10, 3140 (2019).
  * Minder et al. [2019] M. Minder, M. Pittaluga, G. Roberts, M. Lucamarini, J. Dynes, Z. Yuan, and A. Shields, Experimental quantum key distribution beyond the repeaterless secret key capacity, Nat. Photonics 13, 334 (2019).
  * Liu et al. [2019] Y. Liu, Z.-W. Yu, W. Zhang, J.-Y. Guan, J.-P. Chen, C. Zhang, X.-L. Hu, H. Li, C. Jiang, J. Lin, T.-Y. Chen, L. You, Z. Wang, X.-B. Wang, Q. Zhang, and J.-W. Pan, Experimental twin-field quantum key distribution through sending or not sending, Phys. Rev. Lett. 123, 100505 (2019).
  * Zhong et al. [2019] X. Zhong, J. Hu, M. Curty, L. Qian, and H.-K. Lo, Proof-of-principle experimental demonstration of twin-field type quantum key distribution, Phys. Rev. Lett. 123, 100506 (2019).
  * Zhong et al. [2021] X. Zhong, W. Wang, L. Qian, and H.-K. Lo, Proof-of-principle experimental demonstration of twin-field quantum key distribution over optical channels with asymmetric losses, npj Quantum Information 7, 8 (2021).
  * Tomamichel et al. [2012] M. Tomamichel, C. C. W. Lim, N. Gisin, and R. Renner, Tight finite-key analysis for quantum cryptography, Nat. Commun. 3, 634 (2012).
  * Grasselli et al. [2018] F. Grasselli, H. Kampermann, and D. Bruß, Finite-key effects in multipartite quantum key distribution protocols, New J. Phys. 20, 113014 (2018).
  * Yin et al. [2020] H.-L. Yin, M.-G. Zhou, J. Gu, Y.-M. Xie, Y.-S. Lu, and Z.-B. Chen, Tight security bounds for decoy-state quantum key distribution, Sci. Rep. 10, 14312 (2020).
  * Yin and Chen [2019b] H.-L. Yin and Z.-B. Chen, Finite-key analysis for twin-field quantum key distribution with composable security, Sci. Rep. 9, 17113 (2019b).
  * Müller-Quade and Renner [2009] J. Müller-Quade and R. Renner, Composability in quantum cryptography, New J. Phys. 11, 085006 (2009).
  * Canetti [2001] R. Canetti, Universally composable security: a new paradigm for cryptographic protocols, in Proceedings 42nd IEEE Symposium on Foundations of Computer Science (2001) pp. 136–145.
  * Lütkenhaus [1999] N. Lütkenhaus, Estimates for practical quantum cryptography, Phys. Rev. A 59, 3301 (1999).