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arXiv:quant-ph/0506125

Numerical simulation of Bell inequality's violation using optical transverse modes in multimode waveguides

Jian Bo Fu, Xun Zhang

Published Jun 15, 2005• 0 citations
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Abstract

We numerically demonstrate that "mode-entangled states" based on the transverse modes of classical optical fields in multimode waveguides violate Bell's inequality. Numerically simulating the correlation measurement scheme of Bell's inequality, we obtain the normalized correlation functions of the intensity fluctuations for the two entangled classical fields. By using the correlation functions, the maximum violations of Bell's inequality are obtained. This implies that the two classical fields in the mode-entangled states, although spatially separated, present a nonlocal correlation.

DOI
10.48550/arxiv.quant-ph/0506125

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We numerically demonstrate that "mode-entangled states" based on the transverse modes of classical optical fields in multimode waveguides violate Bell's inequality. Numerically simulating the correlation measurement scheme of Bell's inequality, we obtain the normalized correlation functions of the intensity fluctuations for the two entangled classical fields. By using the correlation functions, the maximum violations of Bell's inequality are obtained. This implies that the two classical fields in the mode-entangled states, although spatially separated, present a nonlocal correlation.
We numerically demonstrate that ‘mode-entangled states’ based on the transverse modes of classical optical fields in multimode waveguides violate Bell's inequality. Numerically simulating the correlation measurement scheme of Bell's inequality, we obtain the normalized correlation functions of the intensity fluctuations for the two entangled classical fields. By using the correlation functions, the maximum violations of Bell's inequality are obtained. This implies that the two classical fields in the mode-entangled states, although spatially separated, present a nonlocal correlation.
We discuss ``mode-entangled states'' based on the optical transverse modes of the optical field propagating in multimode waveguides, which are classical simulation of the quantum entangled states. The simulation is discussed in detail, including the violation of the Bell inequality and the correlation properties of optical pulses' group delays. The research on this simulation may be important, for it not only provides useful insights into fundamental features of quantum entanglement, but also yields interesting insights into quantum computation and quantum communication.
It is theoretically and experimentally shown that photons emitted by statistically independent incoherent classical light sources and measured in the far field in spatially separated modes may display spatial correlations akin to path-entanglement of photons produced by quantum sources. By measuring higher order photon-correlations at different locations, i.e., mmm photons in one mode and one photon in another mode, we experimentally demonstrate for m≥6m \geq 6m≥6 a violation of Bell-type inequalities for spatial degrees of freedom. The spatial correlations among the photons can be understood from state projection where the detection of the first mmm photons projects the sources onto a state which emits the subsequent photon in a strongly correlated manner. From this perspective the entanglement and violation of Bell's inequalities appears as a consequence of nonvanishing cross correlations between noncommuting quadrature phase components of the two spatially separated fields after mmm photons have been recorded. In this way we show that classical systems may produce spatial field correlations violating local realistic theories.
We show that nonlocal correlation experiments on the two spatially separated modes of a maximally path-entangled number state may be performed. They lead to a violation of a Clauser-Horne Bell inequality for any finite photon number NNN. We also present an analytical expression for the two-mode Wigner function of a maximally path-entangled number state and investigate a Clauser-Horne-Shimony-Holt Bell inequality for such a state. We test other Bell-type inequalities. Some are violated by a constant amount for any NNN.
We consider the entanglement of orthogonal generalized Bernoulli states in two separate single-mode high-QQQ cavities. The expectation values and the correlations of the electric field in the cavities are obtained. We then define, in each cavity, a dichotomic operator expressible in terms of the field states which can be, in principle, experimentally measured by a probe atom that ``reads'' the field. Using the quantum correlations of couples of these operators, we construct a Bell's inequality which is shown to be violated for a wide range of the degree of entanglement and which can be tested in a simple way. Thus the cavity fields directly show quantum nonlocal properties. A scheme is also sketched to generate entangled orthogonal generalized Bernoulli states in the two separate cavities.