Relating different quantum generalizations of the conditional Renyi entropy

被引：61

作者：

Tomamichel, Marco ^{[1
,2
]}

Berta, Mario ^{[3
,4
]}

Hayashi, Masahito ^{[1
,5
]}

机构：

[1] Natl Univ Singapore, Ctr Quantum Technol, Singapore 117543, Singapore

[2] Univ Sydney, Sch Phys, Sydney, NSW 2006, Australia

[3] CALTECH, Inst Quantum Informat & Matter, Pasadena, CA 91125 USA

[4] Swiss Fed Inst Technol, Inst Theoret Phys, CH-8092 Zurich, Switzerland

[5] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 464860, Japan

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2014年 / 55卷 / 08期

基金：

新加坡国家研究基金会;

关键词：

PRIVACY AMPLIFICATION; INFORMATION; CAPACITY;

D O I：

10.1063/1.4892761

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Recently a new quantum generalization of the Renyi divergence and the corresponding conditional Renyi entropies was proposed. Here, we report on a surprising relation between conditional Renyi entropies based on this new generalization and conditional Renyi entropies based on the quantum relative Renyi entropy that was used in previous literature. Our result generalizes the well-known duality relation H(A broken vertical bar B) + H(A broken vertical bar C)= 0 of the conditional von Neumann entropy for tripartite pure states to Renyi entropies of two different kinds. As a direct application, we prove a collection of inequalities that relate different conditional Renyi entropies and derive a new entropic uncertainty relation. (C) 2014 AIP Publishing LLC.

引用

页数：10

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