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arXiv:2410.09900 · Physica Scripta

Bounds on multipartite nonlocality via reduction to biased nonlocality

Hafiza Rumlah Amer, Jibran Rashid

Published Feb 16, 2026• 0 citations
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Abstract

Abstract Multipartite information principles are needed to understand nonlocal quantum correlations. Towards that end, we provide optimal bounds on genuine multipartite nonlocality for classes of THRESHOLD games using the LOCCG (Local Operations and Classical Communication with Grouping) model. Our proof develops a reduction between multipartite nonlocal and biased bipartite nonlocal games. Generalizing this reduction to a larger class of games may build a bridge from multipartite to bipartite principles.

DOI
10.1088/1402-4896/ae4657

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Abstract Multipartite information principles are needed to understand nonlocal quantum correlations. Towards that end, we provide optimal bounds on genuine multipartite nonlocality for classes of THRESHOLD games using the LOCCG (Local Operations and Classical Communication with Grouping) model. Our proof develops a reduction between multipartite nonlocal and biased bipartite nonlocal games. Generalizing this reduction to a larger class of games may build a bridge from multipartite to bipartite principles.
We introduce a feature of no-signaling (Bell) nonlocal theories: namely, when a system of multiple parties manifests genuine nonlocal correlation, then there cannot be arbitrarily high nonlocal correlation among any subset of the parties. We call this feature complementarity of genuine multipartite nonlocality. We use Svetlichny's criterion for genuine multipartite nonlocality and nonlocal games to derive the complementarity relations under no-signaling constraints. We find that the complementarity relations are tightened for the much stricter quantum constraints. We compare this notion with the well-known notion of monogamy of nonlocality. As a consequence, we obtain tighter nontrivial monogamy relations that take into account genuine multipartite nonlocality. Furthermore, we provide numerical evidence showcasing this feature using a bipartite measure and several other well-known tripartite measures of nonlocality.
Local measurements on bipartite maximally entangled states can yield correlations that are maximally nonlocal, monogamous, and with fully random outcomes. This makes these states ideal for bipartite cryptographic tasks. Genuine-multipartite nonlocality constitutes a stronger notion of nonlocality in the multipartite case. Maximal genuine-multipartite nonlocality, monogamy, and random outcomes are thus highly desired properties for genuine-multipartite cryptographic scenarios. We prove that local measurements on any Greenberger-Horne-Zeilinger state can produce correlations that are fully genuine-multipartite nonlocal, monogamous, and with fully random outcomes. A key ingredient in our proof is a multipartite chained Bell inequality detecting genuine-multipartite nonlocality, which we introduce. Finally, we discuss applications to device-independent secret sharing.
Genuine multpartite quantum nonlocality can be quantified by the communication cost needed to reproduce the nonlocal correlation by classical communication models. This prompts the question as to how one may provide such an operational characterization for the nonclassicality of local multipartite correlations arising from genuinely quantum states possessing quantum discord. To answer this question, we consider a classical simulation protocol where one of the parties pre-share a random variable with the other parties who may also share arbitrary randomness. We demonstrate that genuine nonclassicality of local multipartite correlations is necessary for implying genuine superlocality which is the requirement for a larger dimension of the random variable in the above classical simulation protocol than that of quantum state that can generate the nonclassical correlations.
Abstract The violations of Bell inequalities by measurements on quantum states give rise to the phenomenon of quantum non-locality and express the advantage of using quantum resources over classical ones for certain information-theoretic tasks. The relative degree of quantum violations has been well studied in the bipartite scenario and in the multipartite scenario with respect to fully local behaviours. However, the multipartite setting entails a more complex classification in which different notions on non-locality can be established. In particular, genuine multipartite non-local distributions apprehend truly multipartite effects, given that these behaviours cannot be reproduced by bilocal models that allow correlations among strict subsets of the parties beyond a local common cause. We show here that, while in the so-called correlation scenario the relative violation of bilocal Bell inequalities by quantum resources is bounded, i.e. it does not grow arbitrarily with the number of inputs, it turns out to be unbounded in the general case. We identify Bell functionals that take the form of non-local games for which the ratio of the quantum and bilocal values grows unboundedly as a function of the number of inputs and outputs.
Quantum physics provides results at information processing tasks that are unattainable by any classical theory. The aim of this thesis is to identify and characterize quantum entanglement and quantum nonlocality, the key resources used at quantum information protocols. We consider the problem of finding better experimental schemes to detect entangled states. For that, we study approximate physical realizations to non-physical processes, which provide the most efficient method to identify entanglement. We prove that many of these physical approximations have a simple experimental implementation. We then study characterization of quantum nonlocality. We introduce a method using the multipartite scenario, where more than two parties are involved, which provides several results on bipartite and multipartite quantum nonlocality. First, we prove that there exist quantum states which contain full multipartite nonlocality, which consist of the strongest kind of nonlocality. then, we prove that the combined use of several copies of a state can activate its nonlocal properties. In particular, this holds for bipartite and genuine multipartite nonlocality. Finally, we characterize quantum nonlocality by distinguishing it from stronger-than-quantum nonlocality. We construct a multipartite game for which classical and quantum players perform equally well, but for which supre-quantum players can sometimes provide an advantage. Our results suggest that physical resources might obbey a generalized no-signaling principle ( according to which ther's no instantaneous communication).
The violations of Bell inequalities by measurements on quantum states give rise to the phenomenon of quantum non-locality and express the advantage of using quantum resources over classical ones for certain information-theoretic tasks. The relative degree of quantum violations has been well studied in the bipartite scenario and in the multipartite scenario with respect to fully local behaviours. However, the multipartite setting entails a more complex classification in which different notions on non-locality can be established. In particular, genuine multipartite non-local distributions apprehend truly multipartite effects, given that these behaviours cannot be reproduced by bilocal models that allow correlations among strict subsets of the parties beyond a local common cause. We show here that, while in the so-called correlation scenario the relative violation of bilocal Bell inequalities by quantum resources is bounded, i.e. it does not grow arbitrarily with the number of inputs, it turns out to be unbounded in the general case. We identify Bell functionals that take the form of non-local games for which the ratio of the quantum and bilocal values grows unboundedly as a function of the number of inputs and outputs.