On a sufficient condition for additivity in quantum information theory

N. Datta; A. S. Holevo; Yu M. Suhov

doi:10.1007/s11122-005-0013-7

On a sufficient condition for additivity in quantum information theory

N. Datta
, A. S. Holevo
, Yu M. Suhov

Mathematics

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

8 Scopus citations

Abstract

In this paper we give a sufficient condition for additivity of the minimum output entropy for a pair of given channels and an analytic verification of this condition for specific quantum channels breaking a closely related multiplicativity property [1, 2]. This yields validity of the additivity conjecture for these channels, a result obtained by a different method in [3]. Our proof relies heavily upon certain concavity properties of the output entropy, which are of independent interest.

Original language	English (US)
Pages (from-to)	76-90
Number of pages	15
Journal	Problems of Information Transmission
Volume	41
Issue number	2
DOIs	https://doi.org/10.1007/s11122-005-0013-7
State	Published - Apr 2005

All Science Journal Classification (ASJC) codes

Information Systems
Computer Science Applications
Computer Networks and Communications

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10.1007/s11122-005-0013-7

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title = "On a sufficient condition for additivity in quantum information theory",

abstract = "In this paper we give a sufficient condition for additivity of the minimum output entropy for a pair of given channels and an analytic verification of this condition for specific quantum channels breaking a closely related multiplicativity property [1, 2]. This yields validity of the additivity conjecture for these channels, a result obtained by a different method in [3]. Our proof relies heavily upon certain concavity properties of the output entropy, which are of independent interest.",

author = "N. Datta and Holevo, \{A. S.\} and Suhov, \{Yu M.\}",

note = "Funding Information: 1 This work was initiated when the second author was an overseas visiting scholar at St John{\textquoteright}s College, Cam-bridge. Afterwards he was supported by the Russian Scientific School Program, project no. 1758.2003.1. The first and third authors worked in association with the CMI, University of Cambridge – MIT. 2 It is known that the χ-capacity of a channel in a d-dimensional space is attained on an ensemble of at most d2 states. Thus, this estimate was shown to be tight for qubit channels (d = 2).",

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doi = "10.1007/s11122-005-0013-7",

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AU - Holevo, A. S.

AU - Suhov, Yu M.

N1 - Funding Information: 1 This work was initiated when the second author was an overseas visiting scholar at St John’s College, Cam-bridge. Afterwards he was supported by the Russian Scientific School Program, project no. 1758.2003.1. The first and third authors worked in association with the CMI, University of Cambridge – MIT. 2 It is known that the χ-capacity of a channel in a d-dimensional space is attained on an ensemble of at most d2 states. Thus, this estimate was shown to be tight for qubit channels (d = 2).

PY - 2005/4

Y1 - 2005/4

N2 - In this paper we give a sufficient condition for additivity of the minimum output entropy for a pair of given channels and an analytic verification of this condition for specific quantum channels breaking a closely related multiplicativity property [1, 2]. This yields validity of the additivity conjecture for these channels, a result obtained by a different method in [3]. Our proof relies heavily upon certain concavity properties of the output entropy, which are of independent interest.

AB - In this paper we give a sufficient condition for additivity of the minimum output entropy for a pair of given channels and an analytic verification of this condition for specific quantum channels breaking a closely related multiplicativity property [1, 2]. This yields validity of the additivity conjecture for these channels, a result obtained by a different method in [3]. Our proof relies heavily upon certain concavity properties of the output entropy, which are of independent interest.

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JO - Problems of Information Transmission

JF - Problems of Information Transmission

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ER -

On a sufficient condition for additivity in quantum information theory

Abstract

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