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Probl. Peredachi Inf., 2014, Volume 50, Issue 3, Pages 35–50 (Mi ppi2143)  

This article is cited in 5 scientific papers (total in 5 papers)

Information Theory

On superactivation of one-shot zero-error quantum capacity and the related property of quantum measurements

M. E. Shirokova, T. V. Shulmanb

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b University of Copenhagen, Copenhagen, Denmark

Abstract: We give a detailed description of a low-dimensional quantum channel (input dimension 4, Choi rank 3) demonstrating the symmetric form of superactivation of one-shot quantum zero-error capacity. This property means appearance of a noiseless (perfectly reversible) subchannel in the tensor square of a channel having no noiseless subchannels. Then we describe a quantum channel with an arbitrary given level of symmetric superactivation (including the infinite value). We also show that superactivation of one-shot quantum zero-error capacity of a channel can be reformulated in terms of quantum measurement theory as appearance of an indistinguishable subspace for the tensor product of two observables having no indistinguishable subspaces.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00295-а
12-01-00319-а
Russian Academy of Sciences - Federal Agency for Scientific Organizations


Full text: PDF file (285 kB)
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English version:
Problems of Information Transmission, 2014, 50:3, 232–246

Bibliographic databases:

UDC: 621.391.1+519.72
Received: 03.03.2014

Citation: M. E. Shirokov, T. V. Shulman, “On superactivation of one-shot zero-error quantum capacity and the related property of quantum measurements”, Probl. Peredachi Inf., 50:3 (2014), 35–50; Problems Inform. Transmission, 50:3 (2014), 232–246

Citation in format AMSBIB
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\paper On superactivation of one-shot zero-error quantum capacity and the related property of quantum measurements
\jour Probl. Peredachi Inf.
\yr 2014
\vol 50
\issue 3
\pages 35--50
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3273850}
\transl
\jour Problems Inform. Transmission
\yr 2014
\vol 50
\issue 3
\pages 232--246
\crossref{https://doi.org/10.1134/S003294601403003X}
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    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, “On quantum zero-error capacity”, Russian Math. Surveys, 70:1 (2015), 176–178  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. M. E. Shirokov, “On multipartite superactivation of quantum channel capacities”, Problems Inform. Transmission, 51:2 (2015), 87–102  mathnet  crossref  mathscinet  isi  elib
    3. Shirokov M.E., “on Channels With Positive Quantum Zero-Error Capacity Having Vanishing N-Shot Capacity”, Quantum Inf. Process., 14:8 (2015), 3057–3074  crossref  mathscinet  zmath  isi  elib  scopus
    4. G. G. Amosov, I. Yu. Zhdanovskii, “Structure of the Algebra Generated by a Noncommutative Operator Graph which Demonstrates the Superactivation Phenomenon for Zero-Error Capacity”, Math. Notes, 99:6 (2016), 924–927  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. J. Levick, D. W. Kribs, R. Pereira, “Quantum Privacy and Schur Product Channels”, Rep. Math. Phys., 80:3 (2017), 333–347  crossref  mathscinet  zmath  isi
  • Проблемы передачи информации Problems of Information Transmission
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