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Quantum hypothesis testing with group symmetry

J. Math. Phys. 50, 103304 (2009); doi:10.1063/1.3234186

Published 22 October 2009

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Fumio Hiai,1 Milán Mosonyi,2,3 and Masahito Hayashi1
1Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai 980-8579, Japan
2Centre for Quantum Technologies, National University of Singapore, Science Drive 2, Singapore 117543, Singapore
3Mathematical Institute, Budapest University of Technology and Economics, Egry József u 1, Budapest 1111, Hungary
The asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system. We consider various asymptotic error exponents in connection with the problems of the Chernoff bound, the Hoeffding bound, and Stein's lemma, and derive bounds on these quantities in terms of their corresponding statistical distance measures. A special emphasis is put on the comparison of the performances of group-invariant and unrestricted measurements. ©2009 American Institute of Physics
History: Received 16 April 2009; accepted 10 August 2009; published 22 October 2009
Permalink: http://link.aip.org/link/?JMAPAQ/50/103304/1
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KEYWORDS and PACS

Keywords
PACS
  • 03.65.Ta
    Foundations of quantum mechanics; measurement theory
  • 05.70.Ce
    Thermodynamic functions and equations of state
  • 03.67.Mn
    Entanglement measures, witnesses, and other characterizations (quantum information)
  • 02.20.-a
    Group theory
  • 03.65.Fd
    Algebraic methods in quantum mechanics
  • 03.65.Ud
    Entanglement and quantum nonlocality
  • YEAR: 2009

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PUBLICATION DATA

ISSN:
0022-2488 (print)   1089-7658 (online)
Publisher:
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