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arXiv:quant-ph/0103014

Simulation of Einstein-Podolsky-Rosen experiments in a local hidden variables model with limited efficiency and coherence

Werner A. Hofer

Published Mar 4, 2001• 2 citations
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Abstract

We simulate correlation measurements of entangled photons numerically. The model employed is strictly local. The correlation is determined by its classical expression with one decisive difference: we sum up coincidences for each pair individually. We analyze the effects of decoherence, detector efficiency and polarizer thresholds in detail. The Bell inequalities are violated in these simulations. The violation depends crucially on the threshold of the polarizer switches and can reach a value of 2.0 in the limiting case. Existing experiments can be fully accounted for by limited coherence and non-ideal detector switches. It seems thus safe to conclude that the Bell inequalities are no suitable criterium to decide on the nonlocality issue.

DOI
10.48550/arxiv.quant-ph/0103014

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We simulate correlation measurements of entangled photons numerically. The model employed is strictly local. The correlation is determined by its classical expression with one decisive difference: we sum up coincidences for each pair individually. We analyze the effects of decoherence, detector efficiency and polarizer thresholds in detail. The Bell inequalities are violated in these simulations. The violation depends crucially on the threshold of the polarizer switches and can reach a value of 2.0 in the limiting case. Existing experiments can be fully accounted for by limited coherence and non-ideal detector switches. It seems thus safe to conclude that the Bell inequalities are no suitable criterium to decide on the nonlocality issue.
We simulate correlation measurements of entangled photons numerically. The model employed is strictly local. In our model correlations arise from a phase, connecting the electromagnetic fields of the two photons at their separate points of measurement. We sum up coincidences for each pair individually and model the operation of a polarizer beam splitter numerically. The results thus obtained differ substantially from the classical results. In addition, we analyze the effects of decoherence and non-ideal beam splitters. It is shown that under realistic experimental conditions the Bell inequalities are violated by more than 30 standard deviations.
The violation of Bell's inequalities in Einstein-Podolsky-Rosen experiments has been demonstrated for photons and ions. In all experiments of this kind the relation between visibility, efficiency, and Bell violation is generally unknown. In this paper we show that simulations based on a local hidden variables models for entangled photons provide this information. It is established that these properties are closely related by the way, in which photons are detected after a polarizer beam splitter. On this basis we suggest controlled experiments which, for the first time, subject the superposition principle to experimental tests.
The demonstration and use of nonlocality, as defined by Bell's theorem, rely strongly on dealing with nondetection events due to losses and detectors'inefficiencies. Otherwise, the so-called detection loophole could be exploited. The only way to avoid this is to have detection efficiencies that are above a certain threshold. We introduce the intermediate assumption of limited detection efficiency, that is, in each run of the experiment, the overall detection efficiency is lower bounded by η(min)>0. Hence, in an adversarial scenario, the adversaries have arbitrary large but not full control over the inefficiencies. We analyze the set of possible correlations that satisfy limited detection locality and show that they necessarily satisfy some linear Bell-like inequalities. We prove that quantum theory predicts the violation of one of these inequalities for all η(min)>0. Hence, nonlocality can be demonstrated with arbitrarily small limited detection efficiencies. We validate this assumption experimentally via a twin-photon implementation in which two users are provided with one photon each out of a partially entangled pair. We exploit on each side a passive switch followed by two measurement devices with fixed settings. Assuming the switches are not fully controlled by an adversary, nor by hypothetical local variables, we reveal the nonlocality of the established correlations despite a low overall detection efficiency.
In the derivation of Bell's inequalities, probability distribution is supposed to be a function of only hidden variable. We point out that the true implication of the probability distribution of Bell's correlation function is the distribution of the joint measurement outcomes on the two sides. So it is a function of both hidden variable and settings. In this case, Bell's inequalities fail. Our further analysis shows that Bell's locality holds neither for dependent events nor for independent events. We think that the measurements of EPR pairs are dependent events, thus violation of Bell's inequalities cannot rule out the existence of local hidden variable. In order to explain the results of EPR-type experiments, we suppose that polarization entangled photon pair can be composed of two circularly or linearly polarized photons with correlated hidden variables, and a couple of experiments of quantum measurement are proposed. The first uses delayed measurement on one photon of the EPR pair to demonstrate directly whether measurement on the other could have any non-local influence on it. Then several experiments are suggested to reveal the components of polarization entangled photon pair. The last one uses successive polarization measurements on a pair of EPR photons to show that two photons with a same quantum state will behave in the same way under the same measuring condition.
In derivating of Bell’s inequalities, the probability distribution is supposed to be a function only of a hidden variable. We point out that the true implication of the probability distribution of Bell’s correlation function is the distribution of joint measurement outcomes on the two sides. It is therefore a function of both the hidden variable and the settings. In this case, Bell’s inequalities fail. Our further analysis shows that Bell’s locality holds neither for dependent events nor for independent events. We think that the measurements of EPR pairs are dependent events, and hence violation of Bell’s inequalities cannot rule out the existence of local hidden variable. To explain the results of EPR-type experiments, we suppose that a polarization-entangled photon pair can be composed of two circularly or linearly polarized photons with correlated hidden variables, and a couple of experiments of quantum measurement are proposed. The first uses delayed measurement on one photon of the EPR pair to demonstrate directly whether measurement on the other could have any nonlocal influence on it. Then several experiments are suggested to reveal the components of the polarization-entangled photon pair. The last one uses successive polarization measurements on a pair of EPR photons to show that two photons with the same quantum state behave the same under the same measuring conditions.
Generalizations of Bell's inequalities for Einstein Podolsky and Rosen entangled correlations for arbitrary spin s are discussed.Violations of local realism and the classical limit of quantum nonlocality for large s are discussed.The role of the polarization and of the spin alignment in the violation of the Bell inequalities are investigated.A Bayes analysis of entangled correlations is performed using the nonlocal quantum distribution.The local but nonpositive Einstein Podolsky and Rosen quantum distribution is investigated in the limit when s → .The classical limit of the quantum Malus 1aw for arbitrary spin s is formulated in terms of the spin patl integrals.