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Physical Review A

Correlated photon asymmetry in local realism

Stuart Mirell

Published Jul 1, 1994• 3 citations
Publisher

Abstract

Agreement with quantum theory and experiment exists for locally real models violating the apparently plausible additional assumptions of Bell inequalities subject to the use of low-efficiency detectors. A locally real optical hidden-variable model of this class is constructed here with asymmetric correlated photon pairs from the physical basis of Malus's law. The model introduces no arbitrary constants, naturally violates factorization and no enhancement, predicts a 1/${3\mathrm{c}\mathrm{o}\mathrm{s}}^{2}$\ensuremath{\theta} joint probability for high-efficiency detectors, and is testable with currently available low-efficiency detectors.

DOI
10.1103/physreva.50.839

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Agreement with quantum theory and experiment exists for locally real models violating the apparently plausible additional assumptions of Bell inequalities subject to the use of low-efficiency detectors. A locally real optical hidden-variable model of this class is constructed here with asymmetric correlated photon pairs from the physical basis of Malus's law. The model introduces no arbitrary constants, naturally violates factorization and no enhancement, predicts a 1/3cos2{3\mathrm{c}\mathrm{o}\mathrm{s}}^{2}3cos2\ensuremath{\theta} joint probability for high-efficiency detectors, and is testable with currently available low-efficiency detectors.
This letter challenges the standard interpretation of Bell test results, which has been used to argue for the abandonment of local realism. We demonstrate that the quantum-mechanical correlation Pc (θ) = cos2 (θ) and the classical Malus' Law result Pc (θ) = 1/2 cos2 (θ) + 1/4 are not contradictory but are complementary descriptions of two distinct source preparations. By modeling light as a real transverse electromagnetic wave, we identify the initial phase orientation of the wavefront as a local hidden variable. Stochastic (randomly prepared) photon sources produce four equally likely phase combinations, yielding the full Malus' Law distribution. Correlated sources, however, are physically constrained to produce only the synchronized subset of these combinations, yielding the cos2 (θ) correlation. We argue that standard Bell test analysis conflates these distinct populations and violates the Fair Sampling Assumption, rendering Bell's inequality inapplicable to the aggregated data. The observed "quantum" correlation is therefore the signature of a correlated source producing pre-synchronized wavefronts, not evidence of non-local communication. We conclude that local realism remains a viable, classical framework for describing these phenomena.
A locally real representation is derived from projections in Hilbert space without arbitrary constants. The inherent enhancement property of the resultant states removes restriction by Bell's theorem. Exact agreement with quantum mechanics is demonstrated by explicit calculations of photon transmission in Malus's law, joint detection probability for correlated photons, spin 12\frac{1}{2}21​ particle transmission through successive Stern-Gerlach analyzers, and joint detection probability for correlated spin 12\frac{1}{2}21​ particles. The representation is experimentally testable with respect to quantum mechanics.
A local hidden-variable model is exhibited for the experiments by Aspect, Grangier, and Roger [Phys. Rev. Lett. 47, 460 (1981); 49, 91 (1982)] and Aspect, Dalibard, and Roger [Phys. Rev. Lett. 49, 1804 (1982)] measuring polarization correlation of optical-photon pairs. The model agrees with quantum-mechanical predictions for all measurable quantities even with ideal polarizers and detectors, and emphasizes the need of a high degree of directional correlation, besides the correlation of spin (or polarization or other quantities), in any test of locality. It is proved that homogeneous inequalities, involving only coincidence detection rates, cannot discriminate between quantum mechanics and local theories, which invalidates all previously used empirical tests. The role of supplementary assumptions, like the so-called no enhancement, for the derivation of Bell's inequalities is discussed. Finally it is conjectured that quantum mechanics might be compatible with local realism, if we assume that not all self-adjoint operators represent observables and not all density operators represent states.
Stochastic optics may be considered as simply a local realistic interpretation of quantum optics and, in this sense, it is a first step in the reinterpretation of the whole of quantum theory. However, as it is not possible to interpret all the details of quantum theory in a local realistic manner, as shown by Bell's theorem, minor changes are introduced in the formalism with the consequence that the new theory makes different predictions in some special cases. In stochastic optics, the quantum-operator formalism is simply considered a formal way of dealing with stochastic fields. In particular, the quantum zero point is taken as a real random electromagnetic radiation filling the whole of space. This radiation noise has the same nature as light signals, the only difference being the greater intensity of the latter. We assume that photon detectors have an intensity threshold just above the level of the noise, thus detecting only signals. Transmission of radiation through polarizers follows Malus's law, but the interplay of signal and noise leads quite naturally to the prediction that the detection probability of some signals is enhanced, which is known to be a necessary condition for the violation of the empirically tested Bell inequalities. In our view, correlated photon pairs are pairs of light signals supercorrelated in polarization, in the sense that, as well as the signal, the accompanying noise is also correlated. Thus stochastic optics allows predictions for the empirical correlations very close, but not identical, to the quantum ones. The theory is applied to the analysis of all experiments designed to test the Bell inequalities by measuring polarization correlations of photon pairs. The predictions agree with quantum optics and experiments within statistical errors, except for the Holt-Pipkin experiment. In this case, the experimental results agree with stochastic optical predictions within two standard deviations while violating quantum optics by four.
A local hidden-variable model is constructed for the postselected correlations of nonmaximally entangled photon pairs in the states |Phi_r> and |Psi_r>, continuous in r over [-1,1] from the product state to the maximally entangled state. Its root-mean-square deviations from the quantum correlations and from the coincidence probabilities, averaged over a uniform grid of polarizer angles, are 0.0322 and 0.0233, smaller than those of the sigmoid-threshold model of Ref. [14] by factors of 2.7 to 3.5. The source emits a photon pair with a probability that depends on the hidden variable and on r; each station detects with a probability that depends on the local hidden variable and on the local polarizer angle. This dependence violates the fair-sampling assumption and exploits the detection loophole. On the postselected sample the model violates the CHSH inequality for |Phi_r>, reaching 2*sqrt(2) at |r|=1, with single-detector efficiency ≈ 85%, outside the assumptions of both the CHSH inequality and Mermin's 82.8% efficiency bound. The CH--Eberhard parameter, which does not assume fair sampling, satisfies J<0 over the full entanglement range.