Locality and orthomodular structure of compound systems

Mirko Navara

Pavel Pták, Sylvia Pulmannová

A. R. Marlow

Teppei Watanabe

A P-lattice is defined as a σ-complete, orthomodular atomic lattice ℒ which is formed by the set of propositions of a physical system. A composition of physical systems in the framework of P-lattices is considered and some notions of locality are given. It is shown that the following statements about compound systems are equivalent. (a) All atoms of a compound system are reducible to those of its subsystems. (b) All pure states of a compound system are separable into those of its subsystems. (c) A compound system has statistical property independence. (d) At least one of the subsystems is classical. (e) Bell-type inequalities hold.

Boris Ischi

Teppei Watanabe

A P-lattice is a σ-complete, orthomodular atomic lattice ℒ which is formed by the set of propositions of a physical system. A composition of physical systems is considered, and some concept of locality in a compound physical system is represented in terms of P-lattices. We give a remark toward necessary and sufficient conditions for it to hold, which have been provided implicitly in antecedent studies, and we show that it can be provided under weaker conditions.