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No-cloning theorem on quantum logics

J. Math. Phys. 50, 102107 (2009); doi:10.1063/1.3245811

Published 20 October 2009

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Takayuki Miyadera1 and Hideki Imai1,2
1Research Center for Information Security (RCIS), National Institute of Advanced Industrial Science and Technology (AIST), Daibiru Building 1003, Sotokanda, Chiyoda-ku, Tokyo 101-0021, Japan
2Graduate School of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan
This paper discusses the no-cloning theorem in a logicoalgebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result, indicating a relation between the cloning on effect algebras and hidden variables. ©2009 American Institute of Physics
History: Received 8 May 2009; accepted 3 September 2009; published 20 October 2009
Permalink: http://link.aip.org/link/?JMAPAQ/50/102107/1
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KEYWORDS and PACS

Keywords
PACS
  • 03.65.Fd
    Algebraic methods in quantum mechanics
  • 02.10.Ab
    Logic and set theory
  • YEAR: 2009

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