Subsystems of a finite quantum system and Bell-like inequalities

8th International Symposium on Quantum Theory and Symmetries

Vourdas, A.^1

Department of Computing, University of Bradford, Bradford BD7 1DP, United Kingdom^1

关键词: Associativity;    Contextuality;    Finite quantum systems;    Heyting algebras;    Logical connectives;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/512/1/012036/pdf
DOI  :  10.1088/1742-6596/512/1/012036

来源: IOP

【 摘 要 】

The set of subsystems Σ(m) of a finite quantum system Σ(n) with variables in (n), together with logical connectives, is a Heyting algebra. The probabilities τ(m|ρn)=Tr[(m)ρn] (where (m) is the projector to Σ(m)) are compatible with associativity of the join in the Heyting algebra, only if the variables belong to the same chain. Consequently, contextuality in the present formalism, has the chains as contexts. Various Bell-like inequalities are discussed. They are violated, and this proves that quantum mechanics is a contextual theory.