No-cloning theorem on quantum logics

Journal Article · Thu Oct 15 00:00:00 EDT 2009 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3245811· OSTI ID:21294384

Miyadera, Takayuki ^[1]; Imai, Hideki ^[1]

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1. Research Center for Information Security (RCIS), National Institute of Advanced Industrial Science and Technology (AIST), Daibiru Building 1003, Sotokanda, Chiyoda-ku, Tokyo 101-0021 (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.

• OSTI ID: 21294384
• Journal Information: Journal of Mathematical Physics, Vol. 50, Issue 10; Other Information: DOI: 10.1063/1.3245811; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
HIDDEN VARIABLES
HILBERT SPACE
MATHEMATICAL OPERATORS
QUANTUM COMPUTERS
QUANTUM MECHANICS