Abstract
The nonlocality of quantum states on a bipartite system is tested by comparing probabilistic outcomes of two local observables of different subsystems. For a fixed observable A of the subsystem its optimal approximate double A′ of the other system is defined such that the probabilistic outcomes of A′ are almost similar to those of the fixed observable A. The case of σ-finite standard von Neumann algebras is considered and the optimal approximate double A′ of an observable A is explicitly determined. The connection between optimal approximate doubles and quantum correlations is explained. Inspired by quantum states with perfect correlation, like Einstein–Podolsky–Rosen states and Bohm states, the nonlocality power of an observable A for general quantum states is defined as the similarity that the outcomes of A look like the properties of the subsystem corresponding to A′. As an application of optimal approximate doubles, maximal Bell correlation of a pure entangled state on is found explicitly.
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