Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2004.00695

The powerfulness of classical correlations

Dardo Goyeneche, Wojciech Bruzda, Ondřej Turek, Daniel Arriscado Alsina, Karol Życzkowski

Published Apr 1, 2020• 1 citation
arXivHTMLPDF

Abstract

Determination of classical and quantum values of bipartite Bell inequalities plays a central role in quantum nonlocality. In this work, we characterize in a simple way bipartite Bell inequalities, free of marginal terms, for which the quantum value can be achieved by considering a classical strategy, for any number of measurement settings and outcomes. These findings naturally generalize known results about nonlocal computation and quantum XOR games. Additionally, our technique allows us to determine the classical value for a wide class of Bell inequalities, having quantum advantage or not, in any bipartite scenario.

Related papers

Bounds on quantum nonlocality

Gláucia Murta

One of the main goals in the study of quantum nonlocality is to determine the maximum violation achieved by quantum correlations in a Bell scenario. However, given a Bell inequality, there is no general algorithm to perform this task. As an intermediate step, the development of efficiently computable bounds has played an important role for the advance of the field. In this thesis we phrase the problem of determining the quantum value of a Bell expression in the framework of computational complexity. Then we present our contributions exploring efficiently computable bounds (based on the spectral norm of some matrices) to the quantum value of a particular class of Bell inequalities: the linear games. We derive several results for the bipartite and the multipartite scenarios.

arXiv:1704.04922•Apr 17, 2017•0 citations

Playing Nonlocal Games with Little to No Shared Randomness

Mingze Xu, Eric Chitambar

Bell nonlocality reveals correlations that cannot be explained by classical models and plays a central role in quantum information theory. In this work, we investigate classical models of Bell nonlocality under restrictions on shared randomness. For bipartite scenarios with bounded shared randomness, the set of classical correlations becomes nonconvex. We characterize the correlations achievable without shared randomness through the simultaneous evaluation of multiple linear Bell functionals. We then extend our analysis to quantum networks by relaxing the standard assumption of source independence. In this setting, the feasibility constraints derived for the bipartite case can be used to certify source dependence, and we further construct nonlinear inequalities that distinguish classical models with correlated sources from correlations achievable in standard quantum networks. As an application, we show that these nonlinear network inequalities give rise to an entropic Bell inequality for bipartite scenarios with limited shared randomness.

quant-pharXiv:2608.07833•Aug 11, 2026•0 citations

All tight correlation Bell inequalities have quantum violations

Llorenç Escolà-Farràs, John Calsamiglia, Andreas Winter

The authors show that tight Bell inequalities always have a quantum violation for any bipartite setting of binary measurements. Operationally, this means that all tight XOR game inequalities can be used to test local realism. In geometric terms, the result shows that any correlation Bell inequality for which the classical and quantum values coincide, does not define a facet of the Bell polytope.

arXiv:1908.06669•Physical Review Research•Feb 24, 2020•7 citations

Bell inequalities from outcome equalities

Ricardo Faleiro, Flavien Hirsch, Emmanuel Zambrini Cruzeiro +1 more

In this work, we study a particular class of Bell inequalities involving only direct equality-comparisons of outcomes. In the bipartite case, the scenario can be interpreted as a natural generalization of full-correlator in- equalities (XOR games) beyond binary outputs. We define the sub-polytope of the local polytope corresponding to this scenario and solve it for several bipartite and multipartite scenarios by leveraging some structural prop- erties. In doing so, we obtain thousands of new tight inequalities, many of which are also facets of the standard local polytope. We also define unanimous Bell inequalities, a particular case of the previous class applied to the multipartite setting in which only full-equality events (all outcomes equal) are considered. We show that such inequalities can always be written as deterministic nonlocal games, and we give a simple multipartite unanimous family and prove its local bound. We show that most of these inequalities admit quantum violations, and we also display aspects of their importance for nonlocality. For instance, we identify examples where such inequalities can act as dimension witnesses, outcome witnesses, witnesses of genuine multipartite nonlocality, as well as being relevant to CHSH. These results show that these simple and elegant inequalities by themselves provide a powerful tool for discovering new Bell inequalities and device-independent witnesses.

quant-pharXiv:2603.17030•Physical Review A•Mar 19, 2026•0 citations

Generalized xor games with d outcomes and the task of nonlocal computation

Ravishankar Ramanathan, Remigiusz Augusiak, Gláucia Murta

Two-party xor games (correlation Bell inequalities with two outcomes per party) are the most studied Bell inequalities, and one of the few classes for which the optimal quantum value is known to be exactly calculable. We study a natural generalization of the binary xor games to the class of linear games with $d>2$ outcomes, and propose an easily computable bound on the quantum value of these games. Many interesting properties such as the impossibility of a quantum strategy to win these games, and the quantum bound on the CHSH game generalized to $d$ outcomes are derived. We also use the proposed bound to prove a large-alphabet generalization of the principle of no quantum advantage in nonlocal computation, showing that quantum theory provides no advantage in the task of nonlocal distributed computation of a class of functions with $d$ outcomes for prime $d$, while general no-signaling boxes do. This task is one of the information-theoretic principles attempting to characterize the set of quantum correlations from amongst general no-signaling ones.

arXiv:1502.02974•Physical Review A•Feb 29, 2016•16 citations

Classifying the simplest Bell inequalities beyond qubits and their applications towards self-testing

Palash Pandya, Shubhayan Sarkar, Remigiusz Augusiak

Bell inequalities reveal the fundamentally nonlocal character of quantum mechanics. In this regard, one of the interesting problems is to explore all possible Bell inequalities that demonstrate a gap between local and nonlocal quantum behaviour. This is useful for the geometric characterisation of the set of nonlocal correlations achievable within quantum theory. Moreover, it provides a systematic way to construct Bell inequalities that are tailored to specific quantum information processing tasks. This characterisation is well understood in the simplest $(2,2,2)$ scenario, namely two parties performing two binary outcome measurements. However, beyond this setting, relatively few Bell inequalities are known, and the situation becomes particularly scarce in scenarios involving a greater number of outcomes. Here, we consider the $(2,2,3)$ scenario, or two parties performing two three-outcome measurements, and characterise all Bell inequalities that can arise from the simplest sum-of-squares decomposition and are maximally violated by the maximally entangled state of local dimension three. We then utilise them to self-test this state, along with a class of three-outcome measurements.

quant-pharXiv:2602.08469•Feb 10, 2026•0 citations
Determination of classical and quantum values of bipartite Bell inequalities plays a central role in quantum nonlocality. In this work, we characterize in a simple way bipartite Bell inequalities, free of marginal terms, for which the quantum value can be achieved by considering a classical strategy, for any number of measurement settings and outcomes. These findings naturally generalize known results about nonlocal computation and quantum XOR games. Additionally, our technique allows us to determine the classical value for a wide class of Bell inequalities, having quantum advantage or not, in any bipartite scenario.
One of the main goals in the study of quantum nonlocality is to determine the maximum violation achieved by quantum correlations in a Bell scenario. However, given a Bell inequality, there is no general algorithm to perform this task. As an intermediate step, the development of efficiently computable bounds has played an important role for the advance of the field. In this thesis we phrase the problem of determining the quantum value of a Bell expression in the framework of computational complexity. Then we present our contributions exploring efficiently computable bounds (based on the spectral norm of some matrices) to the quantum value of a particular class of Bell inequalities: the linear games. We derive several results for the bipartite and the multipartite scenarios.
Bell nonlocality reveals correlations that cannot be explained by classical models and plays a central role in quantum information theory. In this work, we investigate classical models of Bell nonlocality under restrictions on shared randomness. For bipartite scenarios with bounded shared randomness, the set of classical correlations becomes nonconvex. We characterize the correlations achievable without shared randomness through the simultaneous evaluation of multiple linear Bell functionals. We then extend our analysis to quantum networks by relaxing the standard assumption of source independence. In this setting, the feasibility constraints derived for the bipartite case can be used to certify source dependence, and we further construct nonlinear inequalities that distinguish classical models with correlated sources from correlations achievable in standard quantum networks. As an application, we show that these nonlinear network inequalities give rise to an entropic Bell inequality for bipartite scenarios with limited shared randomness.
In this work, we study a particular class of Bell inequalities involving only direct equality-comparisons of outcomes. In the bipartite case, the scenario can be interpreted as a natural generalization of full-correlator in- equalities (XOR games) beyond binary outputs. We define the sub-polytope of the local polytope corresponding to this scenario and solve it for several bipartite and multipartite scenarios by leveraging some structural prop- erties. In doing so, we obtain thousands of new tight inequalities, many of which are also facets of the standard local polytope. We also define unanimous Bell inequalities, a particular case of the previous class applied to the multipartite setting in which only full-equality events (all outcomes equal) are considered. We show that such inequalities can always be written as deterministic nonlocal games, and we give a simple multipartite unanimous family and prove its local bound. We show that most of these inequalities admit quantum violations, and we also display aspects of their importance for nonlocality. For instance, we identify examples where such inequalities can act as dimension witnesses, outcome witnesses, witnesses of genuine multipartite nonlocality, as well as being relevant to CHSH. These results show that these simple and elegant inequalities by themselves provide a powerful tool for discovering new Bell inequalities and device-independent witnesses.
Two-party xor games (correlation Bell inequalities with two outcomes per party) are the most studied Bell inequalities, and one of the few classes for which the optimal quantum value is known to be exactly calculable. We study a natural generalization of the binary xor games to the class of linear games with d>2d>2d>2 outcomes, and propose an easily computable bound on the quantum value of these games. Many interesting properties such as the impossibility of a quantum strategy to win these games, and the quantum bound on the CHSH game generalized to ddd outcomes are derived. We also use the proposed bound to prove a large-alphabet generalization of the principle of no quantum advantage in nonlocal computation, showing that quantum theory provides no advantage in the task of nonlocal distributed computation of a class of functions with ddd outcomes for prime ddd, while general no-signaling boxes do. This task is one of the information-theoretic principles attempting to characterize the set of quantum correlations from amongst general no-signaling ones.
Bell inequalities reveal the fundamentally nonlocal character of quantum mechanics. In this regard, one of the interesting problems is to explore all possible Bell inequalities that demonstrate a gap between local and nonlocal quantum behaviour. This is useful for the geometric characterisation of the set of nonlocal correlations achievable within quantum theory. Moreover, it provides a systematic way to construct Bell inequalities that are tailored to specific quantum information processing tasks. This characterisation is well understood in the simplest (2,2,2)(2,2,2)(2,2,2) scenario, namely two parties performing two binary outcome measurements. However, beyond this setting, relatively few Bell inequalities are known, and the situation becomes particularly scarce in scenarios involving a greater number of outcomes. Here, we consider the (2,2,3)(2,2,3)(2,2,3) scenario, or two parties performing two three-outcome measurements, and characterise all Bell inequalities that can arise from the simplest sum-of-squares decomposition and are maximally violated by the maximally entangled state of local dimension three. We then utilise them to self-test this state, along with a class of three-outcome measurements.