No-Cloning Theorem on Quantum Logics

Details No-Cloning Theorem on Quantum Logics No-Cloning Theorem on Quantum Logics

2009-04-21

arxiv.org/abs/0904.3229v3

J. Math. Phys. 50, 102107 (2009)

Physics

Quantum Physics

To appear in J. Math. Phys

Scientific paper

10.1063/1.3245811

This paper discusses the no-cloning theorem in a logico-algebraic 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 cloning on effect algebras and hidden variables.

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