Maximal Parrondo’s Paradox for Classical and Quantum Markov Chains
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  • 作者:F. Alberto Grünbaum ; Michael Pejic
  • 关键词:Primary 60F99 ; Secondary 81Q12 ; 60G10 ; 60J05 ; Parrondo’s paradox ; quantum Parrondo’s paradox ; quantum Markov process
  • 刊名:Letters in Mathematical Physics
  • 出版年:2016
  • 出版时间:February 2016
  • 年:2016
  • 卷:106
  • 期:2
  • 页码:251-267
  • 全文大小:501 KB
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  • 作者单位:F. Alberto Grünbaum (1)
    Michael Pejic (2)

    1. University of California, Berkeley, CA, USA
    2. Berkeley Department of Mathematics, University of California, 970 Evans Hall #3840, Berkeley, CA, 94720-3840, USA
  • 刊物类别:Physics and Astronomy
  • 刊物主题:Physics
    Mathematical and Computational Physics
    Statistical Physics
    Geometry
    Group Theory and Generalizations
  • 出版者:Springer Netherlands
  • ISSN:1573-0530
文摘
Parrondo’s paradox refers to the situation where two, multi-round games with a fixed winning criteria, both with probability greater than one-half for one player to win, are combined. Using a possibly biased coin to determine the rule to employ for each round, paradoxically, the previously losing player now wins the combined game with probability greater than one-half. In this paper, we will analyze classical observed, classical hidden, and quantum versions of a game that displays this paradox. The game we have utilized is simpler than games for which this behavior has been previously noted in the classical and quantum cases. We will show that in certain situations the paradox can occur to a greater degree in the quantum version than is possible in the classical versions. Keywords Parrondo’s paradox quantum Parrondo’s paradox quantum Markov process
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