One experimental arrangement with four detectors per photon implements two distinct probability spaces for Bell tests, and yields new conditional-probability Bell inequalities.
A possible statistics loophole in Bell's theorem
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abstract
Bell's theorem proves the incompatibility between quantum mechanics and local realistic hidden-variable theories. In this paper we show that, contrary to a common belief, the theoretical proof of Bell's theorem is not affected by counterfactual reasoning. Then, we demonstrate that the experimental verification of this theorem may be affected in an unknowable way by our ignorance about the probability distribution of the hidden variables. Our study is based on the standard theory of random variables, and lays the groundwork for a critical rethinking of Bell's theorem and its consequences.
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Generalized measurements for Bell tests in different probability spaces
One experimental arrangement with four detectors per photon implements two distinct probability spaces for Bell tests, and yields new conditional-probability Bell inequalities.