Continuity of the relative entropy of resource

被引：1

作者：

Lami, Ludovico ^{[1
,2
]}

Shirokov, Maksim ^{[3
,4
]}

机构：

[1] Univ Amsterdam, Korteweg de Vries Inst Math, Inst Theoret Phys, Amsterdam, Netherlands

[2] Univ Amsterdam, QuSoft, Amsterdam, Netherlands

[3] Steklov Math Inst, Moscow, Russia

[4] Moscow Inst Phys & Technol, Moscow, Russia

来源：

INTERNATIONAL JOURNAL OF QUANTUM INFORMATION | 2024年 / 22卷 / 05期

关键词：

Quantum state; free state; quantum channel; quantum relative entropy; relative entropy of pi-entanglement; weak*-topology on the set of trace class operators; CRITERION;

D O I：

10.1142/S0219749924400094

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We present a criterion to establish the local continuity of the relative entropy of resource, i.e. the relative entropy distance to the set of free states, in any quantum resource theory. Several basic corollaries of this criterion are presented. Applications to the relative entropy of entanglement in multipartite quantum systems are considered. It is shown, in particular, that local continuity of any relative entropy of multipartite entanglement follows from local continuity of the quantum mutual information.

引用

页码：1 / 14

页数：14

共 50 条

[21] RELATIVE ENTROPY AND RELATIVE CONDITIONAL ENTROPY WITH INFINITE PARTITIONS
Asadiyan, Mohamad Hosein
Ebrahimzadeh, Abolfazl
ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2015, (35): : 319 - 326
[22] Sharp continuity bounds for entropy and conditional entropy
Chen, ZhiHua
Ma, ZhiHao
Nikoufar, Ismail
Fei, Shao-Ming
SCIENCE CHINA-PHYSICS MECHANICS & ASTRONOMY, 2017, 60 (02)
[23] Sharp continuity bounds for entropy and conditional entropy
Zhi Hua Chen
Zhi Hao Ma
Ismail Nikoufar
Shao-Ming Fei
Science China(Physics,Mechanics & Astronomy), 2017, Mechanics & Astronomy)2017 (02) : 70 - 74
[24] ON THE RELATIVE ENTROPY
DONALD, MJ
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1986, 105 (01) : 13 - 34
[25] Floral resource continuity boosts bumble bee colony performance relative to variable floral resources
Hemberger, Jeremy
Witynski, Grant
Gratton, Claudio
ECOLOGICAL ENTOMOLOGY, 2022, 47 (04) : 703 - 712
[26] Continuity of the von Neumann Entropy
M. E. Shirokov
Communications in Mathematical Physics, 2010, 296 : 625 - 654
[27] Continuity of entropy for bimodal maps
Alseda, L
Manosas, F
Mumbru, P
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1995, 52 : 547 - 567
[28] Continuity of entropy for Lorenz maps
Cooperband, Z.
Pearse, E. P. J.
Quackenbush, B.
Rowley, J.
Samuel, T.
West, M.
INDAGATIONES MATHEMATICAE-NEW SERIES, 2020, 31 (01): : 96 - 105
[29] Continuity of the von Neumann Entropy
Shirokov, M. E.
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2010, 296 (03) : 625 - 654
[30] Continuity properties of folding entropy
Liao, Gang
Wang, Shirou
ISRAEL JOURNAL OF MATHEMATICS, 2024,

← 1 2 3 4 5 →