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arXiv:quant-ph/0508024

Homodyne detection and parametric down-conversion: a classical approach applied to proposed "loophole-free" Bell tests

Caroline H. Thompson

Published Aug 2, 2005• 0 citations
arXivHTMLPDF

Abstract

A classical model is presented for the features of parametric down-conversion and homodyne detection relevant to recent proposed ``loophole-free'' Bell tests. The Bell tests themselves are uncontroversial: there are no obvious loopholes that might cause bias and hence, if the world does, after all, obey local realism, no violation of a Bell inequality will be observed. Interest centres around the question of whether or not the proposed criterion for ``non-classical'' light is valid. If cit is not, then the experiments will fail in their initial concept, since both quantum theorists and local realists will agree that we are seeing a purely classical effect. The Bell test, though, is not the only criterion by which the quantum-mechanical and local realist models can be judged. If the experiments are extended by including a range of parameter values and by analysing, in addition to the proposed digitised voltage differences, the raw voltages, the models can be compared in their overall performance and plausibility.

DOI
10.48550/arxiv.quant-ph/0508024

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A classical model is presented for the features of parametric down-conversion and homodyne detection relevant to recent proposed loophole-free'' Bell tests. The Bell tests themselves are uncontroversial: there are no obvious loopholes that might cause bias and hence, if the world does, after all, obey local realism, no violation of a Bell inequality will be observed. Interest centres around the question of whether or not the proposed criterion for non-classical'' light is valid. If cit is not, then the experiments will fail in their initial concept, since both quantum theorists and local realists will agree that we are seeing a purely classical effect. The Bell test, though, is not the only criterion by which the quantum-mechanical and local realist models can be judged. If the experiments are extended by including a range of parameter values and by analysing, in addition to the proposed digitised voltage differences, the raw voltages, the models can be compared in their overall performance and plausibility.
Recent proposed ``loophole-free'' Bell tests are discussed in the light of classical models for the relevant features of optical parametric amplification and homodyne detection. The Bell tests themselves are uncontroversial: there are no obvious loopholes that might cause bias and hence, if the world does, after all, obey local realism, no violation of a Bell inequality will be observed. Interest centres around the question of whether or not the proposed criterion for ``non-classical'' light is valid. If it is not, then the experiments will fail in their initial concept, since both quantum theorists and local realists will agree that we are seeing a purely classical effect. The Bell test, though, is not the only criterion by which the quantum-mechanical and local realist models can be judged. It is suggested that the quantum-mechanical models given in the proposals will also fail in their detailed predictions. If the experiments are extended by including a range of parameter values and by analysing, in addition to the proposed digitised voltage differences, the raw voltages, the models can be compared in their overall performance and plausibility.
It has long been known that the "detection loophole", present when detector efficiencies are below a critical figure, could open the way for alternative "local realist" explanations for the violation of Bell tests. It has in recent years become common to assume the loophole can be ignored, regardless of which version of the Bell test is employed. A simple model is presented that illustrates that this may not be justified. Two of the versions -- the standard test of form -2 <= S <= 2 and the currently-popular "visibility" test -- are at grave risk of bias. Statements implying that experimental evidence "refutes local realism" or shows that the quantum world really is "weird" should be reviewed. The detection loophole is on its own unlikely to account for more than one or two test violations, but when taken in conjunction with other loopholes (briefly discussed) it is seen that the experiments refute only a narrow class of "local hidden variable" models, applicable to idealised situations, not to the real world. The full class of local realist models provides straightforward explanations not only for the publicised Bell-test violations but also for some lesser-known "anomalies".
Abstract. Bell inequalities are intended to show that local realist theories cannot describe the world. A local realist theory is one where physical properties are defined prior to and independent of measurement, and no physical influence can propagate faster than the speed of light. Quantum-mechanical predictions for certain experiments violate the Bell inequality while a local realist theory cannot, and this shows that a local realist theory cannot give those quantum-mechanical predictions. However, because of unexpected circumstances or “loopholes ” in available experiment tests, local realist theories can reproduce the data from these experiments. This paper reviews such loopholes, what effect they have on Bell inequality tests, and how to avoid them in experiment. Avoiding all these simultaneously in one experiment, usually called a “loophole-free ” or “definitive ” Bell test, remains an open task, but is very important for technological tasks such as device-independent security of quantum cryptography, and ultimately for our understanding of the world. ar X iv
Bell inequalities are intended to show that local realist theories cannot describe the world. A local realist theory is one where physical properties are defined prior to and independent of measurement, and no physical influence can propagate faster than the speed of light. Quantum-mechanical predictions for certain experiments violate the Bell inequality while a local realist theory cannot, and this shows that a local realist theory cannot give those quantum-mechanical predictions. However, because of unexpected circumstances or 'loopholes' in available experiment tests, local realist theories can reproduce the data from these experiments. This paper reviews such loopholes, what effect they have on Bell inequality tests, and how to avoid them in experiment. Avoiding all these simultaneously in one experiment, usually called a 'loophole-free' or 'definitive' Bell test, remains an open task, but is very important for technological tasks such as device-independent security of quantum cryptography, and ultimately for our understanding of the world. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.
It has long been known that the "detection loophole", present when detector efficiencies are below a critical figure, could open the way for alternative "local realist" explanations for the violation of Bell tests. It has in recent years become common to assume the loophole can be ignored, regardless of which version of the Bell test is employed. A simple model is presented that illustrates that this may not be justified. Two of the versions -- the standard test of form -2 <= S <= 2 and the currently-popular "visibility" test -- are at grave risk of bias. Statements implying that experimental evidence "refutes local realism" or shows that the quantum world really is "weird" should be reviewed. The detection loophole is on its own unlikely to account for more than one or two test violations, but when taken in conjunction with other loopholes (briefly discussed) it is seen that the experiments refute only a narrow class of "local hidden variable" models, applicable to idealised situations, not to the real world. The full class of local realist models provides straightforward explanations not only for the publicised Bell-test violations but also for some lesser-known "anomalies".
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.