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arXiv:1205.0878 · International Journal of Modern Physics B

ARE QUANTUM CORRELATIONS GENUINELY QUANTUM?

Antonio Di Lorenzo

Published Nov 1, 2012• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1142/s0217979213450161

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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.
A specific instantiation of classical correlation from entangled quantum resources can be established at a distance through the use of local measurements without classical communication. It is thereby possible to, e.g., allow distant entities to randomly combine forces on a course of action which is an element of a predetermined set of possible actions. When this protocol is used, no one knows which action has been chosen. The protocol is intrinsically secure in the same sense as a one-time pad. The entities must have a shared entanglement resource, be able to measure that resource in a predetermined reference frame, and know what they must do to carry out all of the possible actions.
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.
We give a sufficient condition of nonlocality in order to reproduce singlet spin correlations. For a given pair of hidden variables and measurement directions this condition determines only the product of the outcomes and reproduces statistical correlations for all measurement directions; but fails to give a complete description of sub-systems, provides no means to calculate all joint probabilities and puts no constraints on signaling. In order to complete the model we introduce an additional condition. In this case we observe that the character of the nonlocality changes (outcome independence is violated) and nonlocality applies asymmetrically to the spacelike separated parties. At first sight it seems possible to explain this asymmetry by assuming that the observer that measures first determines his outcome locally. However this assumption has no meaning without adopting a privileged reference frame.
If nonlocality is to be inferred from a violation of Bell's inequality, an important assumption is that the measurement settings are freely chosen by the observers, or alternatively, that they are random and uncorrelated with the hypothetical local variables. We demonstrate a connection between models that weaken this assumption, allowing partial correlation, and (i) models that allow classical communication between the distant parties, (ii) models that exploit the detection loophole. Even if Bob's choices are completely independent, all correlations from projective measurements on a singlet can be reproduced, with mutual information between Alice's choice and local variables less than or equal to one bit.
It is well known that entangled quantum states are nonlocal: the corrrelations between local measurements carried out on these states cannot be reproduced by local hidden variable models. Svetlichny, followed by others, showed that multipartite quantum states are more nonlocal than bipartite ones in the sense that even some nonlocal classical models with (super-luminal) communication between some of the parties cannot reproduce the quantum correlations. Here we study in detail the kinds of nonlocality present in quantum states. More precisely, we enquire what kinds of classical communication patterns cannot reproduce quantum correlations. By studying the extremal points of the space of all multiparty probability distributions, in which all parties can make one of a pair of measurements each with two possible outcomes, we find a necessary condition for classical nonlocal models to reproduce the statistics of all quantum states. This condition extends and generalizes work of Svetlichny and others in which it was showed that a particular class of classical nonlocal models, the ``separable'' models, cannot reproduce the statistics of all multiparticle quantum states. Our condition shows that the nonlocality present in some entangled multiparticle quantum states is much stronger than previously thought. We also study the sufficiency of our condition.
Bell’s theorem teaches us that there are quantum correlations that can not be simulated by just shared randomness (Local Hidden variable). There are some recent results which simulate singlet correlation by using either 1 cbit or a binary (no-signaling) correlation which violate Bell’s inequality maximally. But there is one more possible way to simulate quantum correlation by relaxing the condition of independency of measurement on shared randomness. Recently, MJW Hall showed that the statistics of singlet state can be generated by sacrificing measurement independence where underlying distribution of hidden variables depend on measurement direction of both parties [Phys. Rev. Lett.105 250404 (2010)]. He also proved that for any model of singlet correlation, 86 % measurement independence is optimal. In this paper, we show that 59 % measurement independence is optimal for simulating singlet correlation when the underlying distribution of hidden variables depend only on measurements of one party. We also show that a distribution corresponding to this optimal lack of free will, already exists in literature which first appeared in the context of detection efficiency loophole. I.