Semidefinite Programming Strong Converse Bounds for Classical Capacity

doi:10.1109/TIT.2017.2741101

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	Semidefinite Programming Strong Converse Bounds for Classical Capacity
	Wang, Xin 1; Xie, Wei 1; Duan, Runyao 1,2
	2018
发表期刊	IEEE TRANSACTIONS ON INFORMATION THEORY
ISSN	0018-9448
卷号	64 期号:1 页码:640-653
摘要	We 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.
关键词	Classical capacity quantum channel semidefinite programming strong converse zero-error capacity
DOI	10.1109/TIT.2017.2741101
语种	英语
资助项目	Australian Research Council[DP120103776] ; Australian Research Council[FT120100449]
WOS研究方向	Computer Science ; Engineering
WOS类目	Computer Science, Information Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:000418754100038
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/29212
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Xin
作者单位	1.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
推荐引用方式 GB/T 7714	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.