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arXiv:2012.01739

A model independent study of nonlocality with polarization entangled photons

Boya Xie, Sheng Feng

Published Dec 3, 2020• 0 citations
arXivHTMLPDF

Abstract

Nonlocality as a fundamental aspect of quantum mechanics is witnessed by violation of Bell inequality or its variants, for which all relevant studies assume some correlations exhibited by local realistic theories. The strategy of Bell's theorem is to establish some criteria to distinguish local realistic theories from quantum mechanics with respect to the nonlocal nature of entangled systems. Here we propose a model independent study of nonlocality that needs not to assume any local theory since observation of the expected nonlocal effect is straightforward quantum mechanically. Our proposal involves a bipartite polarization-entangled system in which one photon immediately reduces into a circular-polarization (CP) state when its partner at a space-like distance is detected in another CP state. The state reduction of the photon can be mechanically monitored because a CP photon carries angular momentum and exerts a torque on a half-wave plate whose mechanical motion is measurable, which is well described by quantum mechanics and independent of any local realistic assumption.

DOI
10.48550/arxiv.2012.01739

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Nonlocality as a fundamental aspect of quantum mechanics is witnessed by violation of Bell inequality or its variants, for which all relevant studies assume some correlations exhibited by local realistic theories. The strategy of Bell's theorem is to establish some criteria to distinguish local realistic theories from quantum mechanics with respect to the nonlocal nature of entangled systems. Here we propose a model independent study of nonlocality that needs not to assume any local theory since observation of the expected nonlocal effect is straightforward quantum mechanically. Our proposal involves a bipartite polarization-entangled system in which one photon immediately reduces into a circular-polarization (CP) state when its partner at a space-like distance is detected in another CP state. The state reduction of the photon can be mechanically monitored because a CP photon carries angular momentum and exerts a torque on a half-wave plate whose mechanical motion is measurable, which is well described by quantum mechanics and independent of any local realistic assumption.
We investigate direct observation of quantum nonlocality without reference to theoretical models (including Bell theorem) except quantum mechanics, with a bipartite polarization-entangled state in which one photon immediately reduces into a circular-polarization (CP) state after its partner is detected in another CP state. Of essence is the mechanical detection of the CP state of a photon that carries angular momentum and exerts a torque on a half-wave plate whose mechanical motion is then varied. If implemented, the model-independent observation of quantum nonlocality violates Lorentz invariance in experiment and may indicate new fundamental physics beyond the Standard Model.
Since John Bell has established his famous inequality and several independent experiments have confirmed the distinct polarization correlation of entangled photons predicted by quantum mechanics it is evident that quantum mechanics cannot be explained by local realistic theories. Actually, the observed polarization correlation can be deduced from wave optical considerations. The correlation has its origin in the phase coupling of the two circularly polarized wave packets leaving the photon source simultaneously. The experimental results violate Bell's inequality although no non-local interactions have to be assumed. In consequence the principle of locality remains valid in the scope of quantum mechanics. However, the principle of realism has to be replaced by the less stringent principle of contextuality.
John Bell’s theorem of 1964 states that local elements of physical reality, existing independent of measurement, are inconsistent with the predictions of quantum mechanics (Bell, J. S. (1964), Physics (College. Park. Md). Specifically, correlations between measurement results from distant entangled systems would be smaller than predicted by quantum physics. This is expressed in Bell’s inequalities. Employing modifications of Bell’s inequalities, many experiments have been performed that convincingly support the quantum predictions. Yet, all experiments rely on assumptions, which provide loopholes for a local realist explanation of the measurement. Here we report an experiment with polarization-entangled photons that simultaneously closes the most significant of these loopholes. We use a highly efficient source of entangled photons, distributed these over a distance of 58.5 meters, and implemented rapid random setting generation and high-efficiency detection to observe a violation of a Bell inequality with high statistical significance. The merely statistical probability of our results to occur under local realism is less than 3.74×10-31, corresponding to an 11.5 standard deviation effect.
Entangled photons leaving parametric down-conversion sources exhibit a pronounced polarization correlation. The data violate Bell's inequality thus proving that local realistic theories cannot explain the correlation results. Therefore many physicists are convinced that the correlation can only be brought about by non-local interactions. Some of them even assume that instantaneous influences at a distance are at work. Actually, assuming a strict phase correlation of the photons at the source the observed polarization correlation can be deduced from wave optical considerations. The correlation has its origin in the phase coupling of circularly polarized wave packets leaving the fluorescence photon source simultaneously. The enlargement of the distances between photon source and observers does not alter the correlation if the polarization status of the wave packets accompanying the photons is not changed on their way from the source to the observers. At least with respect to the polarization correlation of entangled photons the principle of locality remains valid.
EPR showed that two particles emitted from a source can be entangled by a shared wavefunction where two non-commuting observables (position, momentum) can be simultaneously real, leading to a contradiction with quantum mechanics (two non-commuting variables can not be simultaneously real). John Bell derived an inequality where any local hidden variables prediction is bounded and quantum mechanics can violate the inequality. Bell tests on correlated photon pairs showed a clear violation of the Bell inequality and agreement with quantum mechanics. This study revealed that the Bell inequality holds at any individual instances in a given system but it does not hold over the entire population. The Bell inequality is not an incompatibility criterion for local hidden variables vs quantum mechanics rather it is a criterion for an individual nature vs population dynamics. The nonlocality prediction given by wavefunction is a system approximation and local causality (photon polarization) provides a complete description of the Bell tests. The paper concludes with great satisfaction that the measurement of two correlated photons at a distance was a local cause (photon-filter interaction did not violate the special theory of relativity).
Entangled quantum systems can connect to the environment via a Bell state measurement. This applies, for example, to teleportation and entanglement swapping. Although the results are well understood, it is not entirely clear whether they involve nonlocal action or whether they are predetermined. This can best be decided from a model, provided it predicts the key measurement results. Models based on the fact that the partners of an entangled pair have the same value of a statistical parameter cannot be applied here. This is because the partner particles of the resulting entangled states after a teleportation or an entanglement swapping never had contact before. The question then is, what connects entangled photons? Therefore, this paper presents a local realistic model that reproduces the quantum mechanical predictions for expectation values with polarization measurements, but is not based on shared statistical parameters. Instead, the coupling of the entangled particles is based on initial conditions and conservation of spin angular momentum. The model refutes Bell's theorem and also explains teleportation and entanglement swapping in a local way. The manuscript is thus a step forward toward a complete theory describing quantum physical reality as thought possible by Einstein, Podolsky, and Rosen.