Bell's inequalities between independent particles

M. Revzen, A. Mann

Bernard Yurke, David Stoler

In the usual Bell's-inequality experiments two particles carrying spin or polarization are prepared in an entangled state generated from the decay of an unstable quantum-mechanical system. These particles are then delivered to spin or polarization analyzers. The statistics of the measurements reported by the analyzers are incompatible with our notions of local realism. Here we show that Bell's-inequality violations occur even when the initial state is a direct product state. In fact, the two particles can come from two independent widely separated sources.

Afshin Shafiee, Mehdi Golshani

It is generally believed that Bell's inequality holds for the case of entangled states, including two correlated particles or special states of a single particle. Here, we derive a single-particle Bell's inequality for two correlated spin states at two successive times, appealing to the statistical independence condition in an ideal experiment, for a locally causal hidden variables theory. We show that regardless of the locality assumption, the inequality can be violated by some quantum predictions.

M. Revzen, A. Mann

Louis Sica

The original Bell inequality was obtained in a statistical derivation assuming three mutually cross-correlated random variables (four in the later version). Given that observations destroy the particles, the physical realization of three variables from an experiment producing two particles per trial requires two separate trial runs. One assumed variable value (for particle 1) occurs at a fixed instrument setting in both trial runs while a second variable (for particle 2) occurs at alternative instrument settings in the two trial runs. Given that measurements on the two particles occurring in each trial are themselves correlated, measurements from independent realizations at mutually exclusive settings on particle 2 are conditionally independent, i.e., conditionally dependent on particle 1, through probability. This situation is realized from variables defined by Bell using entangled particle pairs. Two correlations have the form that Bell computed from entanglement, but a third correlation from conditionally independent measurements has a different form. When the correlations are computed using quantum probabilities, the Bell inequality is satisfied without recourse to assumptions of non-locality, or non-reality.

Thomas E. Kiess