RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Guidelines for authors Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 2007, Volume 52, Issue 2, Pages 301–335 (Mi tvp174)

On properties of quantum channels related to their classical capacity

M. E. Shirokov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: This paper is devoted to further study of the Holevo capacity of infinite-dimensional quantum channels. The existence of a unique optimal average state for a quantum channel constrained by an arbitrary convex set of states is shown. The minimax expression for the Holevo capacity of a constrained channel is obtained. The $\chi$-function and the convex closure of the output entropy of an infinite-dimensional quantum channel are considered. It is shown that the $\chi$-function of an arbitrary channel is lower semicontinuous on the set of all states and has continuous restrictions to subsets of states with continuous output entropy. The explicit expression for the convex closure of the output entropy of an infinite-dimensional quantum channel is obtained and its properties are explored. It is shown that the convex closure of the output entropy coincides with the convex hull of the output entropy on the set of states with finite output entropy and, similarly to the $\chi$-function, it has continuous restrictions to subsets of states with continuous output entropy. The applications of the obtained results to the theory of entanglement are considered. The properties of the convex closure of the output entropy make it possible to generalize some results related to the additivity problem to the infinite-dimensional case.

Keywords: quantum state, entropy, quantum channel, the Holevo capacity, the $\chi$-function, convex closure of the output entropy of a quantum channel.

DOI: https://doi.org/10.4213/tvp174

Full text: PDF file (3708 kB)
References: PDF file   HTML file

English version:
Theory of Probability and its Applications, 2008, 52:2, 250–276

Bibliographic databases:

Citation: M. E. Shirokov, “On properties of quantum channels related to their classical capacity”, Teor. Veroyatnost. i Primenen., 52:2 (2007), 301–335; Theory Probab. Appl., 52:2 (2008), 250–276

Citation in format AMSBIB
\Bibitem{Shi07} \by M.~E.~Shirokov \paper On properties of quantum channels related to their classical capacity \jour Teor. Veroyatnost. i Primenen. \yr 2007 \vol 52 \issue 2 \pages 301--335 \mathnet{http://mi.mathnet.ru/tvp174} \crossref{https://doi.org/10.4213/tvp174} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2742503} \zmath{https://zbmath.org/?q=an:05315075} \elib{http://elibrary.ru/item.asp?id=9511774} \transl \jour Theory Probab. Appl. \yr 2008 \vol 52 \issue 2 \pages 250--276 \crossref{https://doi.org/10.1137/S0040585X97982980} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000261612800004} \elib{http://elibrary.ru/item.asp?id=13594849} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-47849111296} 

• http://mi.mathnet.ru/eng/tvp174
• https://doi.org/10.4213/tvp174
• http://mi.mathnet.ru/eng/tvp/v52/i2/p301

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. M. E. Shirokov, A. S. Holevo, “On Approximation of Infinite-Dimensional Quantum Channels”, Problems Inform. Transmission, 44:2 (2008), 73–90
2. M. E. Shirokov, “On Channels with Finite Holevo Capacity”, Theory Probab. Appl., 53:4 (2009), 648–662
3. M. E. Shirokov, “On properties of the space of quantum states and their application to the construction of entanglement monotones”, Izv. Math., 74:4 (2010), 849–882
4. A. S. Holevo, “Gaussian optimizers and the additivity problem in quantum information theory”, Russian Math. Surveys, 70:2 (2015), 331–367
5. Chanda T., Das T., Mal Sh., Sen(De) Aditi, Sen U., “Canonical Leggett-Garg Inequality: Nonclassicality of Temporal Quantum Correlations Under Energy Constraint”, Phys. Rev. A, 98:2 (2018), 022138
•  Number of views: This page: 320 Full text: 56 References: 53