Semidefinite Programming Strong Converse Bounds for Classical Capacity
Wang, Xin1; Xie, Wei1; Duan, Runyao1,2
AbstractWe investigate the classical communication over quantum channels when assisted by no-signaling and positive-partial-transpose-preserving (PPT) codes, for which both the optimal success probability of a given transmission rate and the one-shot epsilon-error capacity are formalized as semidefinite programs (SDPs). Based on this, we obtain improved SDP finite blocklength converse bounds of general quantum channels for entanglement-assisted codes and unassisted codes. Furthermore, we derive two SDP strong converse bounds for the classical capacity of general quantum channels: for any code with a rate exceeding either of the two bounds of the channel, the success probability vanishes exponentially fast as the number of channel uses increases. In particular, applying our efficiently computable bounds, we derive an improved upper bound on the classical capacity of the amplitude damping channel. We also establish the strong converse property for the classical and private capacities of a new class of quantum channels. We finally study the zero-error setting and provide efficiently computable upper bounds on the one-shot zero-error capacity of a general quantum channel.
KeywordClassical capacity quantum channel semidefinite programming strong converse zero-error capacity
Funding ProjectAustralian Research Council[DP120103776] ; Australian Research Council[FT120100449]
WOS Research AreaComputer Science ; Engineering
WOS SubjectComputer Science, Information Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000418754100038
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Document Type期刊论文
Corresponding AuthorWang, Xin
Affiliation1.Univ Technol Sydney, Fac Engn & Informat Technol, Ctr Quantum Software & Informat, Ultimo, NSW 2007, Australia
2.Chinese Acad Sci, Acad Math & Syst Sci, UTS AMSS Joint Res Lab Quantum Computat & Quantum, Beijing 100190, Peoples R China
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Wang, Xin,Xie, Wei,Duan, Runyao. Semidefinite Programming Strong Converse Bounds for Classical Capacity[J]. IEEE TRANSACTIONS ON INFORMATION THEORY,2018,64(1):640-653.
APA Wang, Xin,Xie, Wei,&Duan, Runyao.(2018).Semidefinite Programming Strong Converse Bounds for Classical Capacity.IEEE TRANSACTIONS ON INFORMATION THEORY,64(1),640-653.
MLA Wang, Xin,et al."Semidefinite Programming Strong Converse Bounds for Classical Capacity".IEEE TRANSACTIONS ON INFORMATION THEORY 64.1(2018):640-653.
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