One-Shot Entanglement-Assisted Quantum and Classical Communication

被引:40
作者
Datta, Nilanjana [1 ]
Hsieh, Min-Hsiu [2 ]
机构
[1] Univ Cambridge, Stat Lab, Cambridge CB3 0WB, England
[2] Univ Technol Sydney, Fac Engn & Informat Technol, Ctr Quantum Computat & Intelligent Syst, Sydney, NSW 2007, Australia
关键词
Entanglement-assisted classical capacity; entanglement assisted quantum capacity; one-shot capacity; CAPACITY; CHANNEL; INFORMATION;
D O I
10.1109/TIT.2012.2228737
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
We study entanglement-assisted quantum and classical communication over a single use of a quantum channel, which itself can correspond to a finite number of uses of a channel with arbitrarily correlated noise. We obtain characterizations of the corresponding one-shot capacities by establishing upper and lower bounds on them in terms of the difference of two smoothed entropic quantities. In the case of a memoryless channel, the upper and lower bounds converge to the known single-letter formulas for the corresponding capacities, in the limit of asymptotically many uses of it. Our results imply that the difference of two smoothed entropic quantities characterizing the one-shot entanglement-assisted capacities serves as a one-shot analog of the mutual information, since it reduces to the mutual information, between the output of the channel and a system purifying its input, in the asymptotic, memoryless scenario.
引用
收藏
页码:1929 / 1939
页数:11
相关论文
共 38 条
[1]   von Neumann capacity of noisy quantum channels [J].
Adami, C ;
Cerf, NJ .
PHYSICAL REVIEW A, 1997, 56 (05) :3470-3483
[2]   On quantum fidelities and channel capacities [J].
Barnum, H ;
Knill, E ;
Nielsen, MA .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2000, 46 (04) :1317-1329
[3]   Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem [J].
Bennett, CH ;
Shor, PW ;
Smolin, JA ;
Thapliyal, AV .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2002, 48 (10) :2637-2655
[4]   The Quantum Reverse Shannon Theorem Based on One-Shot Information Theory [J].
Berta, Mario ;
Christandl, Matthias ;
Renner, Renato .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2011, 306 (03) :579-615
[5]   Quantum capacity of a class of compound channels [J].
Bjelakovic, Igor ;
Boche, Holger ;
Noetzel, Janis .
PHYSICAL REVIEW A, 2008, 78 (04)
[6]   Classical Capacities of Compound and Averaged Quantum Channels [J].
Bjelakovic, Igor ;
Boche, Holger .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2009, 55 (07) :3360-3374
[7]   The Quantum Capacity of Channels With Arbitrarily Correlated Noise [J].
Buscemi, Francesco ;
Datta, Nilanjana .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2010, 56 (03) :1447-1460
[8]   The coding theorem for a class of quantum channels with long-term memory [J].
Datta, Nilanjana ;
Dorlas, Tony C. .
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2007, 40 (28) :8147-8164
[9]   The apex of the family tree of protocols: optimal rates and resource inequalities [J].
Datta, Nilanjana ;
Hsieh, Min-Hsiu .
NEW JOURNAL OF PHYSICS, 2011, 13
[10]   Entanglement assisted classical capacity of a class of quantum channels with long-term memory [J].
Datta, Nilanjana ;
Suhov, Yurii ;
Dorlas, Tony C. .
QUANTUM INFORMATION PROCESSING, 2008, 7 (06) :251-262