KMS Of Academy of mathematics and systems sciences, CAS
On Zero-Error Communication via Quantum Channels in the Presence of Noiseless Feedback | |
Duan, Runyao1,2,3; Severini, Simone4,5; Winter, Andreas6,7 | |
2016-09-01 | |
发表期刊 | IEEE TRANSACTIONS ON INFORMATION THEORY |
ISSN | 0018-9448 |
卷号 | 62期号:9页码:5260-5277 |
摘要 | We initiate the study of zero-error communication via quantum channels when the receiver and the sender have at their disposal a noiseless feedback channel of unlimited quantum capacity, generalizing Shannon's zero-error communication theory with instantaneous feedback. We first show that this capacity is only a function of the linear span of Choi-Kraus operators of the channel, which generalizes the bipartite equivocation graph of a classical channel, and which we dub non-commutative bipartite graph. Then, we go on to show that the feedback-assisted capacity is non-zero (allowing for a constant amount of activating noiseless communication) if and only if the noncommutative bipartite graph is non-trivial, and give a number of equivalent characterizations. This result involves a far-reaching extension of the conclusive exclusion of quantum states. We then present an upper bound on the feedback-assisted zero-error capacity, motivated by a conjecture originally made by Shannon and proved later by Ahlswede. We demonstrate that this bound to have many good properties, including being additive and given by a minimax formula. We also prove a coding theorem showing that this quantity is the entanglement-assisted capacity against an adversarially chosen channel from the set of all channels with the same Choi-Kraus span, which can also be interpreted as the feedback-assisted unambiguous capacity. The proof relies on a generalization of the Postselection Lemma (de Finetti reduction) that allows to reflect additional constraints, and which we believe to be of independent interest. This capacity is a relaxation of the feedback-assisted zero-error capacity; however, we have to leave open the question of whether they coincide in general. We illustrate our ideas with a number of examples, including classical-quantum channels and Weyl diagonal channels, and close with an extensive discussion of open questions. |
关键词 | Quantum information zero-error capacity feedback |
DOI | 10.1109/TIT.2016.2562580 |
语种 | 英语 |
资助项目 | Australian Research Council (ARC)[DP120103776] ; National Natural Science Foundation of China[61179030] ; ARC Future Fellowship[FT120100449] ; Newton International Fellowship ; Royal Society ; U.K. Engineering and Physical Sciences Research Council ; European Commission through STREP project QCS ; European Commission through STREP project RAQUEL ; European Research Council through Advanced Grant Project IRQUAT ; Ministry of Economy and Competitiveness within Fonds Europeen de Developpement Economique et Regional Funds[FIS2008-01236] ; Ministry of Economy and Competitiveness within Fonds Europeen de Developpement Economique et Regional Funds[FIS2013-40627-P] ; Generalitat de Catalunya of the Comissio lnterdepartmental de Recerca i Innovacio Tecnologic[2014 SGR 966] |
WOS研究方向 | Computer Science ; Engineering |
WOS类目 | Computer Science, Information Systems ; Engineering, Electrical & Electronic |
WOS记录号 | WOS:000382442300032 |
出版者 | IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/23601 |
专题 | 中国科学院数学与系统科学研究院 |
通讯作者 | Duan, Runyao |
作者单位 | 1.Univ Technol Sydney, Fac Engn & Informat Technol, Ctr Quantum Computat & Intelligent Syst, Sydney, NSW 2007, Australia 2.Tsinghua Univ, Dept Comp Sci & Technol, State Key Lab Intelligent Technol & Syst, Tsinghua Natl Lab Informat Sci & Technol, Beijing 100084, Peoples R China 3.Chinese Acad Sci, UTS Acad Math & Syst Sci AMSS, Joint Res Lab Quantum Computat & Quantum Informat, AMSS, Beijing 100190, Peoples R China 4.UCL, Dept Comp Sci, Mortimer St, London WC1E 6BT, England 5.Shanghai Jiao Tong Univ, Inst Nat Sci, Shanghai 200240, Peoples R China 6.Univ Autonoma Barcelona, ICREA, ES-08193 Barcelona, Spain 7.Univ Autonoma Barcelona, Dept Fis, Grp Informacio Quant, ES-08193 Barcelona, Spain |
推荐引用方式 GB/T 7714 | Duan, Runyao,Severini, Simone,Winter, Andreas. On Zero-Error Communication via Quantum Channels in the Presence of Noiseless Feedback[J]. IEEE TRANSACTIONS ON INFORMATION THEORY,2016,62(9):5260-5277. |
APA | Duan, Runyao,Severini, Simone,&Winter, Andreas.(2016).On Zero-Error Communication via Quantum Channels in the Presence of Noiseless Feedback.IEEE TRANSACTIONS ON INFORMATION THEORY,62(9),5260-5277. |
MLA | Duan, Runyao,et al."On Zero-Error Communication via Quantum Channels in the Presence of Noiseless Feedback".IEEE TRANSACTIONS ON INFORMATION THEORY 62.9(2016):5260-5277. |
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