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arXiv:quant-ph/0512141

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

Caroline H. Thompson

Published Dec 17, 2005• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.quant-ph/0512141

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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.
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.
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'.
We provide a detailed analysis of the recently proposed setup for a loophole-free test of Bell inequality violation using conditionally generated non-Gaussian states of light and balanced homodyning. In the proposed scheme, a two-mode squeezed vacuum state is de-Gaussified by subtracting a single photon from each mode with the use of an unbalanced beam splitter and a standard low-efficiency single-photon detector. We thoroughly discuss the tolerance of the achievable Bell violation in the various experimentally relevant parameters such as the detector efficiencies, the electronic noise, the mixedness of the initial Gaussian state, and the probability of false triggers. We also consider several alternative schemes involving squeezed states, linear optical elements, conditional photon subtraction, and homodyne detection.
We propose a feasible optical setup allowing for a loophole-free Bell test with efficient homodyne detection. A non-Gaussian entangled state is generated from a two-mode squeezed vacuum by subtracting a single photon from each mode, using beam splitters and standard low-efficiency single-photon detectors. A Bell violation exceeding 1% is achievable with 6 dB squeezed light and a homodyne efficiency around 95%. A detailed feasibility analysis, based upon the recent experimental generation of single-mode non-Gaussian states, suggests that this method opens a promising avenue towards a complete experimental Bell test.
Quantum correlations may violate the Bell inequalities. Most experimental schemes confirming this prediction have been realized in all-optical Bell tests suffering from the detection loophole. Experiments which simultaneously close this loophole and the locality loophole are highly desirable and remain challenging. An approach to loophole-free Bell tests is based on amplification of the entangled photons (i.e., on macroscopic entanglement), for which an optical signal should be easy to detect. However, the macroscopic states are partially indistinguishable by classical detectors. An interesting idea to overcome these limitations is to replace the postselection by an appropriate preselection immediately after the amplification. This is in the spirit of state preprocessing revealing hidden nonlocality. Here, we examine one of the possible preselections, but the presented tools can be used for analysis of other schemes. Filtering methods making the macroscopic entanglement useful for Bell tests and quantum protocols are the subject of an intensive study in the field nowadays.