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Physical Review A

Einstein-Podolsky-Rosen correlations of photons: Quantum-field-theory approach

Paweł Caban

Published Nov 6, 2007• 18 citations
Publisher

Abstract

We formulate a description of Einstein-Podolsky-Rosen-type experiments with photons which is especially convenient in the discussion of questions concerning Lorentz covariance. We classify all Lorentz-covariant two-photon states with sharp momenta and define observables corresponding to measurements of the linear polarization of photons. We also calculate explicitly the Einstein-Podolsky-Rosen correlation function and coincidence rate in the scalar two-photon state.

DOI
10.1103/physreva.76.052102

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We formulate a description of Einstein-Podolsky-Rosen-type experiments with photons which is especially convenient in the discussion of questions concerning Lorentz covariance. We classify all Lorentz-covariant two-photon states with sharp momenta and define observables corresponding to measurements of the linear polarization of photons. We also calculate explicitly the Einstein-Podolsky-Rosen correlation function and coincidence rate in the scalar two-photon state.
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Considering a classical source of light (macroscopic), we propose an experiment, based on the principles of the Einstein-Podolsky-Rosen-Bohm correlation, for which one expects to obtain the same polarization correlation coefficient as the one predicted by the quantum theory, when photons are counted in coincidence. The results of a numerical simulation give good ground to believe that the conjectured experiment is reasonable. So, one may argue that the property of light called polarization, that is manifest at any level — microscopic and macroscopic — and which has a precise description in both, the quantum and the classical theories, leads to coincident results under correspondingly similar experimental procedures. Therefore the EPRB correlation is a consequence of that property of light, independently whether it is viewed as constituted by photons or by electromagnetic waves.
We calculate the joint probabilities and the correlation function in Einstein-Podolsky-Rosen--type experiments with a massive vector boson in the framework of quantum field theory. We report on the strange behavior of the correlation function (and the probabilities)---the correlation function, which in the relativistic case still depends on the particle momenta, for some fixed configurations has local extrema. We also show that relativistic spin-1 particles violate some Bell inequalities more than nonrelativistic ones and that the degree of violation of the Bell inequality is momentum dependent.
Abstract The measurement of the position–momentum Einstein–Podolsky–Rosen (EPR) correlations of a two-photon state is important for many quantum information applications ranging from quantum key distribution to coincidence imaging. However, all the existing techniques for measuring the position–momentum EPR correlations involve coincidence detection and thus suffer from issues that result in less accurate measurements. In this article, we propose and demonstrate an experimental scheme that does not require coincidence detection for measuring the EPR correlations. Our technique works for two-photon states that are pure, irrespective of whether the state is separable or entangled. We theoretically show that if the pure two-photon state satisfies a certain set of conditions then the position–momentum EPR correlations can be obtained by doing the intensity measurements on only one of the photons. We experimentally demonstrate this technique for pure two-photon states produced by type-I spontaneous parametric down-conversion, and to the best of our knowledge, we report the most accurate experimental measurement of position–momentum EPR correlations.
Conventionally, one interprets the correlations observed in Einstein-Podolsky-Rosen experiments by Bell's inequalities and quantum nonlocality. We show, in this paper, that identical correlations arise, if the phase relations of electromagnetic fields are considered. In particular, we proceed from an analysis of a one-photon model. The correlation probability in this case contains a phase relation cos(b - a) between the two settings. In the two photon model the phases of the photon's electromagnetic fields are related at the origin. It is shown that this relation can be translated into a linearity requirement for electromagnetic fields between the two polarizers. Along these lines we compute the correlation integral with an expression conserving linearity. This expression, as shown, correctly describes the measured values. It seems thus that quantum nonlocality can be seen as a combination of boundary conditions on possible electromagnetic fields between the polarizers and a relation of the electromagnetic fields of the two photons via a phase. We expect the same feature to arise in every experiment, where joint probabilities of separate polarization measurements are determined.