The minimum Rényi entropy output of a quantum channel is locally additive

Gilad Gour; Todd Kemp

doi:10.1007/s11005-016-0933-8

The minimum Rényi entropy output of a quantum channel is locally additive

Research output: Contribution to journal › Article › peer-review

Abstract

We show that the minimum Rényi entropy output of a quantum channel is locally additive for Rényi parameter α> 1. While our work extends the results of Gour and Friedland (IEEE Trans. Inf. Theory 59(1):603, 2012) (in which local additivity was proven for α= 1), it is based on several new techniques that incorporate the multiplicative nature of ℓ_p-norms, in contrast to the additivity property of the von-Neumann entropy. Our results demonstrate that the counterexamples to the Rényi additivity conjectures exhibit purely global effects of quantum channels. Interestingly, the approach presented here cannot be extended to Rényi entropies with parameter α< 1.

Original language	English
Pages (from-to)	1131-1155
Number of pages	25
Journal	Letters in Mathematical Physics
Volume	107
Issue number	6
DOIs	https://doi.org/10.1007/s11005-016-0933-8
State	Published - 1 Jun 2017
Externally published	Yes

Keywords

Additivity conjecture
Entropy output
Quantum information
Rényi entroy

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1007/s11005-016-0933-8

Cite this

@article{3d5cda360b1c4b52bb69e966b60d56ac,

title = "The minimum R{\'e}nyi entropy output of a quantum channel is locally additive",

abstract = "We show that the minimum R{\'e}nyi entropy output of a quantum channel is locally additive for R{\'e}nyi parameter α> 1. While our work extends the results of Gour and Friedland (IEEE Trans. Inf. Theory 59(1):603, 2012) (in which local additivity was proven for α= 1), it is based on several new techniques that incorporate the multiplicative nature of ℓp-norms, in contrast to the additivity property of the von-Neumann entropy. Our results demonstrate that the counterexamples to the R{\'e}nyi additivity conjectures exhibit purely global effects of quantum channels. Interestingly, the approach presented here cannot be extended to R{\'e}nyi entropies with parameter α< 1.",

keywords = "Additivity conjecture, Entropy output, Quantum information, R{\'e}nyi entroy",

author = "Gilad Gour and Todd Kemp",

note = "Publisher Copyright: {\textcopyright} 2016, Springer Science+Business Media Dordrecht.",

year = "2017",

month = jun,

day = "1",

doi = "10.1007/s11005-016-0933-8",

language = "الإنجليزيّة",

volume = "107",

pages = "1131--1155",

journal = "Letters in Mathematical Physics",

issn = "0377-9017",

publisher = "Springer Netherlands",

number = "6",

}

TY - JOUR

T1 - The minimum Rényi entropy output of a quantum channel is locally additive

AU - Gour, Gilad

AU - Kemp, Todd

PY - 2017/6/1

Y1 - 2017/6/1

N2 - We show that the minimum Rényi entropy output of a quantum channel is locally additive for Rényi parameter α> 1. While our work extends the results of Gour and Friedland (IEEE Trans. Inf. Theory 59(1):603, 2012) (in which local additivity was proven for α= 1), it is based on several new techniques that incorporate the multiplicative nature of ℓp-norms, in contrast to the additivity property of the von-Neumann entropy. Our results demonstrate that the counterexamples to the Rényi additivity conjectures exhibit purely global effects of quantum channels. Interestingly, the approach presented here cannot be extended to Rényi entropies with parameter α< 1.

AB - We show that the minimum Rényi entropy output of a quantum channel is locally additive for Rényi parameter α> 1. While our work extends the results of Gour and Friedland (IEEE Trans. Inf. Theory 59(1):603, 2012) (in which local additivity was proven for α= 1), it is based on several new techniques that incorporate the multiplicative nature of ℓp-norms, in contrast to the additivity property of the von-Neumann entropy. Our results demonstrate that the counterexamples to the Rényi additivity conjectures exhibit purely global effects of quantum channels. Interestingly, the approach presented here cannot be extended to Rényi entropies with parameter α< 1.

KW - Additivity conjecture

KW - Entropy output

KW - Quantum information

KW - Rényi entroy

UR - http://www.scopus.com/inward/record.url?scp=85003868998&partnerID=8YFLogxK

U2 - 10.1007/s11005-016-0933-8

DO - 10.1007/s11005-016-0933-8

M3 - مقالة

SN - 0377-9017

VL - 107

SP - 1131

EP - 1155

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 6

ER -

The minimum Rényi entropy output of a quantum channel is locally additive

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this