Finite Block Length Analysis on Quantum Coherence Distillation and Incoherent Randomness Extraction

Hayashi，Masahito1; Fang，Kun2; Wang，Kun3

2021

10.1109/TIT.2021.3064009

IEEE TRANSACTIONS ON INFORMATION THEORY   影响因子和分区

0018-9448

1557-9654

We give the first systematic study on the second order asymptotics of the operational task of coherence distillation with and without assistance. In the unassisted setting, we introduce a variant of randomness extraction framework where free incoherent operations are allowed before the incoherent measurement and the randomness extractors. We then show that the maximum number of random bits extractable from a given quantum state is precisely equal to the maximum number of coherent bits distillable from the same state. This relation enables us to derive tight second order expansions of both tasks in the independent and identically distributed setting. Remarkably, the incoherent operation classes that can empower coherence distillation for generic states all admit the same second order expansions, indicating their operational equivalence for coherence distillation in both asymptotic and large block length regimes. We then generalize the above line of research to the assisted setting, arising naturally in bipartite quantum systems where Bob distills coherence from the state at hand, aided by the benevolent Alice possessing the other system. More precisely, we introduce a new assisted incoherent randomness extraction task and establish an exact relation between this task and the assisted coherence distillation. It strengthens the one-shot relation in the unassisted setting and confirms that this cryptographic framework offers a new perspective to the study of quantum coherence distillation. Likewise, this relation yields second order characterizations to the assisted tasks. As by-products, we show the strong converse property of the tasks above from their second order expansions.

Coherence coherence distillation Data mining Entropy incoherent randomness extraction Quantum computing Quantum mechanics Quantum state second order analysis strong converse property Task analysis

SCI ; EI

英语

第一

WOS:000652795200046

20211110073070

Distillation ; Distilleries ; Equivalence classes ; Expansion ; Extraction ; Random processes

Chemical Operations:802.3 ; Food Products Plants and Equipment:822.1 ; Probability Theory:922.1 ; Quantum Theory; Quantum Mechanics:931.4 ; Materials Science:951

COMPUTER SCIENCE

2-s2.0-85102248081

Scopus

1.Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China, Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China, Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China, and the Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan.
2.Institute for Quantum Computing, Baidu Research, Beijing 100193, China and Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada. (e-mail: fangfred11@gmail.com)
3.Institute for Quantum Computing, Baidu Research, Beijing 100193, China and Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China.

Hayashi，Masahito,Fang，Kun,Wang，Kun. Finite Block Length Analysis on Quantum Coherence Distillation and Incoherent Randomness Extraction[J]. IEEE TRANSACTIONS ON INFORMATION THEORY,2021,67:3926-3944.

Hayashi，Masahito,Fang，Kun,&Wang，Kun.(2021).Finite Block Length Analysis on Quantum Coherence Distillation and Incoherent Randomness Extraction.IEEE TRANSACTIONS ON INFORMATION THEORY,67,3926-3944.

Hayashi，Masahito,et al."Finite Block Length Analysis on Quantum Coherence Distillation and Incoherent Randomness Extraction".IEEE TRANSACTIONS ON INFORMATION THEORY 67(2021):3926-3944.