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arXiv:quant-ph/0508238 · International Journal of Modern Physics B

CORRELATIONS IN ENTANGLED STATES

B. C. Sanctuary

Published May 20, 2006• 0 citations
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Abstract

Entangled EPR spin pairs can be treated using the statistical ensemble interpretation of quantum mechanics. As such the singlet state results from an ensemble of spin pairs each with its own specific axis of quantization. This axis acts like a quantum mechanical hidden variable. If the spins lose coherence they disentangle into a mixed state that contains classical correlations. In this paper an infinitesimal phase decoherence is introduced to the singlet state in order to reveal more clearly some of the correlations. It is shown that a singlet state has no classical correlations.

DOI
10.1142/s0217979206034078

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Entangled EPR spin pairs can be treated using the statistical ensemble interpretation of quantum mechanics. As such the singlet state results from an ensemble of spin pairs each with its own specific axis of quantization. This axis acts like a quantum mechanical hidden variable. If the spins lose coherence they disentangle into a mixed state that contains classical correlations. In this paper an infinitesimal phase decoherence is introduced to the singlet state in order to reveal more clearly some of the correlations. It is shown that a singlet state has no classical correlations.
Entangled EPR spin pairs can be treated using the statistical ensemble interpretation of quantum mechanics. As such the singlet state results from an ensemble of spin pairs each with an arbitrary axis of quantization. This axis acts as a quantum mechanical hidden variable. If the spins lose coherence they disentangle into a mixed state. Whether or not the EPR spin pairs retain entanglement or disentangle, however, the statistical ensemble interpretation resolves the EPR paradox and gives a mechanism for quantum "teleportation" without the need for instantaneous action-at-a-distance.
A new pure quantum state, isotropic in spin variables, is defined in an extended spin phase space beyond standard quantum mechanics. It allows to represent the entangled singlet state in separable form. The statistical correlations between Alice and Bob measurements become self correlations between hidden spin values for each particle, together with perfect anti correlation between spin values on the pair. Alice determines through measurement on her particle the value of spin in some direction. Spin in another direction is inferred from Bob measurement on the companion. Bell's inequalities are violated because of the wave like behaviour of quantum systems. In full analogy with the two slit experiment, interference terms between spin field components appear determining the contextual character of quantum distributions of probability.
Abstract We propose a novel class of local deterministic models to explain the correlations observed in entangled singlet quantum states. In these models, hidden variables influence both the entangled pair preparation and the measurement settings, thereby relaxing the measurement independence assumption used in Bell’s theorem. Our model accurately reproduces the expected quantum results and demonstrates that freely chosen measurement settings do not necessarily preclude the possibility of hidden variables inducing correlations between the settings and outcomes. This approach reveals an intricate relationship between local determinism and quantum mechanics, showing that local hidden variable theories can be consistent with the predictions of quantum theory. This result calls into question the conventional interpretation, based on Bell’s inequalities, that local theories are fundamentally incompatible with quantum mechanics.
Disentanglement refers to decoherence that destroys the quantum interference terms between particles as they separate. This process reduces the pure isotropic entangled EPR state to a mixed anisotropic state. Averaging over the ensemble of states leads to correlations between separated particles that satisfies Bell's inequalities. Applying disentanglement to EPR pairs of photons shows that entanglement is characterized by various two-particle symmetry properties. These symmetry properties are destroyed by disentanglement but photon helicity is conserved. This is sufficient to account for the correlations needed to resolve the EPR paradox. Apart from a numerical factor, the functional form for the correlations due to entanglement and disentanglement is identical, thereby making it difficult to distinguish between the two in the current experiments.
It is shown that the probabilities for the spin singlet can be reproduced through classical resources, with no communication between the distant parties, by using merely shared (pseudo-)randomness. If the parties are conscious beings aware of both the hidden-variables and the random mechanism, then one has a conspiracy. If the parties are aware of only the random variables, they may be induced to believe that they are able to send instantaneous information to one another. It is also possible to reproduce the correlations at the price of reducing the detection efficiency. It is further demonstrated that the same probability decomposition could be realized through action-at-a-distance, provided it existed.