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arXiv:2411.07631

Almost-quantum correlations violate the isotropy and homogeneity principles in flat space

A. Fahmi

Published Nov 12, 2024• 0 citations
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Abstract

One of fascinating phenomena of nature is quantum nonlocality, which is observed upon measurements on spacelike entangled systems. However, there are sets of post-quantum models which have stronger correlations than quantum mechanics, wherein instantaneous communication remains impossible. The set of almost quantum correlations is one of post-quantum models which satisfies all kinematic axioms of standard quantum correlations except one, meanwhile they contain correlations slightly stronger than quantum correlations. There arises the natural question whether there is some fundamental principle of nature which can genuinely characterizes quantum correlations. Here, we provide an answer and close this gap by invoking the isotropy and homogeneity principles of the flat space as a conclusive and distinguishing criterion to rule out the almost-quantum correlations model. In particular, to characterize quantum correlations we impose the isotropy and homogeneity symmetry group structure on the almost quantum correlations model and request that the joint probability distributions corresponding to the Born rule remain invariant. We prove that this condition is sufficient (and necessary) to reduce the almost quantum correlations model to quantum mechanics in both bipartite and multipartite systems.

DOI
10.48550/arxiv.2411.07631

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One of fascinating phenomena of nature is quantum nonlocality, which is observed upon measurements on spacelike entangled systems. However, there are sets of post-quantum models which have stronger correlations than quantum mechanics, wherein instantaneous communication remains impossible. The set of almost quantum correlations is one of post-quantum models which satisfies all kinematic axioms of standard quantum correlations except one, meanwhile they contain correlations slightly stronger than quantum correlations. There arises the natural question whether there is some fundamental principle of nature which can genuinely characterizes quantum correlations. Here, we provide an answer and close this gap by invoking the isotropy and homogeneity principles of the flat space as a conclusive and distinguishing criterion to rule out the almost-quantum correlations model. In particular, to characterize quantum correlations we impose the isotropy and homogeneity symmetry group structure on the almost quantum correlations model and request that the joint probability distributions corresponding to the Born rule remain invariant. We prove that this condition is sufficient (and necessary) to reduce the almost quantum correlations model to quantum mechanics in both bipartite and multipartite systems.
One of the fundamental questions in physics concerns the relation between spacetime and quantum entanglement. The spacetime is usually considered as a fixed background physical space, and the quantum entanglement is usually manifested as a ``spooky action at a distance" or the existence of ``nonlocality" in nature. Here, we propose the flat-space isotropy and homogeneity principles as the fundamental criteria for determining the maximum degree of nonlocality of nature. More specifically, we consider abstract and deterministic nonlocal-box models which have stronger correlations than in quantum mechanics, whereas therein instantaneous communication remains impossible. We impose space-symmetry group structures on these models and derive a measure for the degree of space symmetries. Surprisingly, there is a tradeoff or inconsistency between the degree of space symmetries and the degree of nonlocality, where this inconsistency is exactly lifted at the Tsirelson bound, as predicted by quantum physics and also predicted in the experiments. Moreover, we prove this result in the general framework of deterministic nonlocal models and conclude that the probabilistic interpretation of the nonlocal box models is an emergent property of the flat-space symmetries.
To identify which principles characterize quantum correlations, it is essential to understand in which sense this set of correlations differs from that of almost-quantum correlations. We solve this problem by invoking the so-called no-restriction hypothesis, an explicit and natural axiom in many reconstructions of quantum theory stating that the set of possible measurements is the dual of the set of states. We prove that, contrary to quantum correlations, no generalized probabilistic theory satisfying the no-restriction hypothesis is able to reproduce the set of almost-quantum correlations. Therefore, any theory whose correlations are exactly, or very close to, the almost-quantum correlations necessarily requires a rule limiting the possible measurements. Our results suggest that the no-restriction hypothesis may play a fundamental role in singling out the set of quantum correlations among other nonsignaling ones.
Characterizing quantum correlations from physical principles is a central problem in the field of quantum information theory. Entanglement breaks bounds on correlations put forth by Bell's theorem, thus challenging the notion of local causality as a physical principle. A natural relaxation is to study no-signalling as a constraint on joint probability distributions. It was shown that, when considered with respect to so-called locally quantum observables, bipartite nonsignalling correlations never exceed their quantum counterparts; still, such correlations generally do not derive from quantum states. This leaves open the search for additional principles which identify quantum states within the larger set of (collections of) nonsignalling joint probability distributions over locally quantum observables. Here, we suggest a natural generalization of no-signalling in the form of no-disturbance to dilated systems. We prove that nonsignalling joint probability distributions satisfying this extension correspond with bipartite quantum states up to a choice of time orientation in subsystems.
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.
Quantum mechanics is not the unique no-signaling theory which is endowed with stronger-than-classical correlations, and there exists a broad class of no-signaling theories allowing even stronger-than-quantum correlations. The principle of information causality has been suggested to distinguish quantum theory from these nonphysical theories, together with an elegant information-theoretic proof of the quantum bound of two-particle correlations. In this work, we extend this to genuine NNN-particle correlations that cannot be reduced to mixtures of states in which a smaller number of particles are entangled. We first express Svetlichny's inequality in terms of multipartite no-signaling boxes, then prove that the strongest genuine multipartite correlations lead to the maximal violation of information causality. The maximal genuine multipartite correlations under the constraint of information causality is found to be equal to the quantum mechanical bound. This result consolidates information causality as a physical principle defining the possible correlations allowed by nature, and provides intriguing insights into the limits of genuine multipartite correlations in quantum theory.
Quantum mechanics is not the unique no-signaling theory which is endowed with stronger-than-classical correlations, and there exists a broad class of no-signaling theories allowing even stronger-than-quantum correlations. The principle of information causality has been suggested to distinguish quantum theory from these nonphysical theories, together with an elegant information-theoretic proof of the quantum bound of two-particle correlations. In this work, we extend this to genuine NNN-particle correlations that cannot be reduced to mixtures of states in which a smaller number of particles are entangled. We first express Svetlichny's inequality in terms of multipartite no-signaling boxes, then prove that the strongest genuine multipartite correlations lead to the maximal violation of information causality. The maximal genuine multipartite correlations under the constraint of information causality is found to be equal to the quantum mechanical bound. This result consolidates information causality as a physical principle defining the possible correlations allowed by nature, and provides intriguing insights into the limits of genuine multipartite correlations in quantum theory.