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The Western Ontario series in philosophy of science

Do Experimental Violations of Bell Inequalities Require a Nonlocal Interpretation of Quantum Mechanics? II: Analysis à la Bell

Edward S. Fry, Xinmei Qu, Marlan O. Scully

Published Jan 1, 2009• 0 citations
Publisher
DOI
10.1007/978-1-4020-9107-0_10

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The nonlocality inherent in quantum mechanics has been tested experimentally, but the nonlocal interpretation of all the relevant experiments can be challenged. All past tests of Bell's inequalities have required supplementary assumptions, without which the experimental results satisfy the inequalities, in agreement with the notion of local realism. There are basically three loopholes that need to be closed; neither the cascade sources nor the parametric down-conversion sources of correlation photons used to date are capable of closing all of them, even if the detectors used had been 100% efficient. We propose a two-crystal down-conversion source, relying on type-II collinear phase matching, which should permit a violation of Bell's inequalities without the need for supplementary assumptions. As the source can produce a true singletlike state, it is also relevant for quantum cryptographic applications.
At first sight the Aharonov-Bohm effect appears nonlocal, though not in the way EPR/ Bell correlations are generally acknowledged to be nonlocal. This paper applies an analysis of nonlocality to the Aharonov-Bohm effect to show that its peculiarities may be blamed either on a failure of a principle of local action or on a failure of a principle of separability. Different interpretations of quantum mechanics disagree on how blame should be allocated. The parallel between the Aharonov-Bohm effect and violations of Bell inequalities turns out to be so close that a balanced assessment of the nature and significance of quantum nonlocality requires a detailed study of both effects.
A problem in quantum information theory is to find the experimental setup that maximizes the nonlocality of correlations with respect to some suitable measure such as the violation of Bell inequalities. There are however some complications with Bell inequalities. First and foremost it is unfeasible to determine the whole set of Bell inequalities already for a few measurements and thus unfeasible to find the experimental setup maximizing their violation. Second, the Bell violation suffers from an ambiguity stemming from the choice of the normalization of the Bell coefficients. An alternative measure of nonlocality with a direct information-theoretic interpretation is the minimal amount of classical communication required for simulating nonlocal correlations. In the case of many instances simulated in parallel, the minimal communication cost per instance is called nonlocal capacity, and its computation can be reduced to a convex-optimization problem. This quantity can be computed for a higher number of measurements and turns out to be useful for finding the optimal experimental setup. Focusing on the bipartite case, we present a simple method for maximizing the nonlocal capacity over a given configuration space and, in particular, over a set of possible measurements, yielding the corresponding optimal setup. Furthermore, we show that there is a functional relationship between Bell violation and nonlocal capacity. The method is illustrated with numerical tests and compared with the maximization of the violation of CGLMP-type Bell inequalities on the basis of entangled two-qubit as well as two-qutrit states. Remarkably, the anomaly of nonlocality displayed by qutrits turns out to be even stronger if the nonlocal capacity is employed as a measure of nonlocality.