2022-09-25T17:58:56Zhttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_oaipmhoai:ipsj.ixsq.nii.ac.jp:002187782022-06-29T15:00:00Z01164:10193:10905:10966
Bounds on oblivious multiparty quantum communication complexity多人数の量子通信複雑性にける新しい手法enghttp://id.nii.ac.jp/1001/00218670/Technical Reporthttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_action_common_download&item_id=218778&item_no=1&attribute_id=1&file_no=1Copyright (c) 2022 by the Information Processing Society of JapanNagoya UniversityNagoya Universityルガル, フランソワ駿河, 大樹The main conceptual contribution of this technical report is investigating quantum multiparty communication complexity in the setting where communication is oblivious. This requirement, which to our knowledge is satisfied by all quantum multiparty protocols in the literature, means that the communication pattern, and in particular the amount of communication exchanged between each pair of players at each round is fixed independently of the input before the execution of the protocol. We show, for a wide class of functions, how to prove strong lower bounds on their oblivious quantum k-party communication complexity using lower bounds on their two-party communication complexity. We apply this technique to prove tight lower bounds for all symmetric functions, and in particular obtain an optimal Ω(k√n) lower bound on the oblivious quantum k-party communication complexity of the n-bit Set-Disjointness function. We also obtain (nearly) matching upper bounds by examining the optimal protocols for each function. In this technical report, we overview these results and do not give most of the technical proofs.The main conceptual contribution of this technical report is investigating quantum multiparty communication complexity in the setting where communication is oblivious. This requirement, which to our knowledge is satisfied by all quantum multiparty protocols in the literature, means that the communication pattern, and in particular the amount of communication exchanged between each pair of players at each round is fixed independently of the input before the execution of the protocol. We show, for a wide class of functions, how to prove strong lower bounds on their oblivious quantum k-party communication complexity using lower bounds on their two-party communication complexity. We apply this technique to prove tight lower bounds for all symmetric functions, and in particular obtain an optimal Ω(k√n) lower bound on the oblivious quantum k-party communication complexity of the n-bit Set-Disjointness function. We also obtain (nearly) matching upper bounds by examining the optimal protocols for each function. In this technical report, we overview these results and do not give most of the technical proofs.AA12894105量子ソフトウェア（QS）2022-QS-619172022-06-302435-64922022-06-28