On Zero-Error Communication via Quantum Channels in the Presence of Noiseless Feedback
Duan, Runyao1,2,3; Severini, Simone4,5; Winter, Andreas6,7
AbstractWe 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 We then present an upper bound on the feedback-assisted zero-error capacity, motivated by a conjecture originally made by Shannon and proved later by Ahlswede.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.
KeywordQuantum information zero-error capacity feedback
Funding ProjectAustralian 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 Research AreaComputer Science ; Engineering
WOS SubjectComputer Science, Information Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000382442300032
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Document Type期刊论文
Corresponding AuthorDuan, Runyao
Affiliation1.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
Recommended Citation
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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