Beyond Set Theory in Bell Inequality

Bell inequality, nonlocality and analyticity

The Bell and the Clauser-Horne-Shimony-Holt inequalities are shown to hold for both the cases of complex and real analytic nonlocality in the setting parameters of Einstein-Podolsky-Rosen-Bohm experiments for spin 12 particles and photons, in both the deterministic and stochastic cases. Therefore, the theoretical and experimental violation of the inequalities by quantum mechanics excludes all h...

Beyond Nash Bargaining Theory: The Nash Set*

We extend Nash's bargaining theory to non-convex and coalitional problems. This paper investigates the implications of Nash-like axioms for bilateral problems and the properties of consistency and converse consistency over multilateral settings. The result is a characterization of the Nash set of NTU games, defined as the solution concept where each pair of players is splitting the gains from t...

On “ Bell ’ s inequality without alternative settings ”

Cabello has recently (in quant-ph/0210081) observed that " ...an EPR-experiment with a fixed POVM on each particle provides a violation of Bell's inequality without requiring local observers to choose between the alternatives. " In this note I discuss the implications of this observation for tests of locality.

Better Bell Inequality Violation by Collective Measurements

The standard Bell inequality experiments test for violation of local realism by repeatedly making local measurements on individual copies of an entangled quantum state. Here we investigate the possibility of increasing the violation of a Bell inequality by making collective measurements. We show that the nonlocality of bipartite pure entangled states, quantified by their maximal violation of th...

Bipartite Bell Inequality and Maximal Violation