No-Signalling-Assisted Zero-Error Capacity of Quantum Channels and an Information Theoretic Interpretation of the Lovasz Number

doi:10.1109/TIT.2015.2507979

CSpace

	No-Signalling-Assisted Zero-Error Capacity of Quantum Channels and an Information Theoretic Interpretation of the Lovasz Number
	Duan, Runyao 1,2,3,4; Winter, Andreas 5
	2016-02-01
发表期刊	IEEE TRANSACTIONS ON INFORMATION THEORY
ISSN	0018-9448
卷号	62 期号:2 页码:891-914
摘要	We study the one-shot zero-error classical capacity of a quantum channel assisted by quantum no-signalling correlations, and the reverse problem of exact simulation of a prescribed channel by a noiseless classical one. Quantum no-signalling correlations are viewed as two-input and twooutput completely positive and trace preserving maps with linear constraints enforcing that the device cannot signal. Both problems lead to simple semidefinite programmes (SDPs) that depend only on the Choi-Kraus (operator) space of the channel. In particular, we show that the zero-error classical simulation cost is precisely the conditional min-entropy of the Choi-Jamiolkowski matrix of the given channel. The zero-error classical capacity is given by a similar-looking but different SDP; the asymptotic zero-error classical capacity is the regularization of this SDP, and in general, we do not know of any simple form. Interestingly, however, for the class of classical-quantum channels, we show that the asymptotic capacity is given by a much simpler SDP, which coincides with a semidefinite generalization of the fractional packing number suggested earlier by Aram Harrow. This finally results in an operational interpretation of the celebrated Lovasz. function of a graph as the zero-error classical capacity of the graph assisted by quantum no-signalling correlations, the first information theoretic interpretation of the Lovasz number.
关键词	Graph Theory quantum information zero-error information theory
DOI	10.1109/TIT.2015.2507979
语种	英语
资助项目	Australian Research Council (ARC)[DP120103776] ; Spanish MINECO[FIS2008-01236] ; FEDER[FIS2013-40627-P] ; Generalitat de Catalunya CIRIT[2014 SGR 966] ; National Natural Science Foundation of China[61179030] ; ARC Future Fellowship[FT120100449] ; European Commission ; STREPs QCS ; RAQUEL ; European Research Council Advanced Grant IRQUAT ; Philip Leverhulme Trust
WOS研究方向	Computer Science ; Engineering
WOS类目	Computer Science, Information Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:000369309900020
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/21989
专题	中国科学院数学与系统科学研究院
通讯作者	Duan, Runyao; Winter, Andreas
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, Beijing 100084, Peoples R China 3.Tsinghua Univ, Dept Comp Sci & Technol, Tsinghua Natl Lab Informat Sci & Technol, Beijing 100084, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, UTS AMSS Joint Res Lab Quantum Computat & Quantum, Beijing 100190, Peoples R China 5.Univ Autonoma Barcelona, ICREA & Fis Teor Informac & Fenomens Quant, ES-08193 Barcelona, Spain
推荐引用方式 GB/T 7714	Duan, Runyao,Winter, Andreas. No-Signalling-Assisted Zero-Error Capacity of Quantum Channels and an Information Theoretic Interpretation of the Lovasz Number[J]. IEEE TRANSACTIONS ON INFORMATION THEORY,2016,62(2):891-914.
APA	Duan, Runyao,&Winter, Andreas.(2016).No-Signalling-Assisted Zero-Error Capacity of Quantum Channels and an Information Theoretic Interpretation of the Lovasz Number.IEEE TRANSACTIONS ON INFORMATION THEORY,62(2),891-914.
MLA	Duan, Runyao,et al."No-Signalling-Assisted Zero-Error Capacity of Quantum Channels and an Information Theoretic Interpretation of the Lovasz Number".IEEE TRANSACTIONS ON INFORMATION THEORY 62.2(2016):891-914.