© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:2312.15705 · Physical Review A

Measurement incompatibility at both parties unrelated to Bell nonlocality in a two-input and two-output setting

Priya Ghosh, Chirag Srivastava, Swati Choudhary, Ujjwal Sen

Published May 12, 2025• 1 citation

Abstract

Two important ingredients necessary for obtaining Bell nonlocal correlations between two spatially separated parties are an entangled state shared between them and an incompatible set of measurements employed by each of them. However, not all entangled states can give rise to Bell nonlocality. Here, we are interested in a complementary question, regarding the role of the sets of incompatible measurements in enabling Bell nonlocality, for arbitrary entangled states. It is known that for some sets of more than two jointly incompatible measurements performed by one of the parties, there does not exist an entangled state and another set of incompatible measurements for the other party, which will result in Bell nonlocality. However, in the two-input and two-output setting per party, measurement incompatibility at a single party will always guarantee Bell nonlocality. Thus, it is interesting to ask whether all sets of incompatible measurements at both parties, in the two-input and two-output setting per party, will result in Bell nonlocality for some shared state. We first observe that Bell nonlocality can always be established when both parties employ any set of incompatible projective measurements. On the other hand, going beyond projective measurements, we present a class of incompatible positive operator-valued measures, employed by both observers, which can never activate Bell nonlocality. Furthermore, we find a sufficient criterion for achieving Bell nonlocal correlations given a fixed amount of pure two-qubit entanglement and a fixed amount of incompatibility of projective measurements applied by either both parties or a single party.

DOI: 10.1103/physreva.111.052208

Related papers

Quantum measurement incompatibility does not imply Bell nonlocality

Flavien Hirsch, Marco Túlio Quintino, Nicolas Brunner

We discuss the connection between the incompatibility of quantum measurements, as captured by the notion of joint measurability, and the violation of Bell inequalities. Specifically, we explicitly present a given set of non-jointly-measurable positive-operator-value measures (POVMs) ${\mathcal{M}}_{A}$ with the following property. Considering a bipartite Bell test where Alice uses ${\mathcal{M}}_{A}$, then for any possible shared entangled state $\ensuremath{\rho}$ and any set of (possibly infinitely many) POVMs ${\mathcal{N}}_{B}$ performed by Bob, the resulting statistics admits a local model and can thus never violate any Bell inequality. This shows that quantum measurement incompatibility does not imply Bell nonlocality in general.

arXiv:1707.06960•Physical Review A•Jan 25, 2018•79 citations

All Incompatible Measurements on Qubits Lead to Multiparticle Bell Nonlocality

Martin Plávala, Otfried Gühne, Marco Túlio Quintino

Bell nonlocality is a fundamental phenomenon of quantum physics as well as an essential resource for various tasks in quantum information processing. It is known that for the observation of nonlocality the measurements on a quantum system have to be incompatible, but the question of which incompatible measurements are useful, remained open. Here we prove that any set of incompatible measurements on qubits leads to a violation of a suitable Bell inequality in a multiparticle scenario, where all parties perform the same set of measurements. Since there exists incompatible measurements on qubits which do not lead to Bell nonlocality for two particles, our results demonstrate a fundamental difference between two-particle and multiparticle nonlocality, pointing at the superactivation of measurement incompatibility as a resource. In addition, our results imply that measurement incompatibility for qubits can always be certified in a device-independent manner.

arXiv:2403.10564•Physical Review Letters•May 21, 2025•6 citations

All Incompatible Sets of Measurements Can Generate Nonlocality Using Quantum Inputs

Andrés F. Ducuara, Patryk Lipka-Bartosik, Cristian E. Susa +1 more

The presence of Bell nonlocality in the correlations arising from measuring spatially separated systems guarantees that the sets of measurements used are necessarily incompatible. Not all sets of incompatible measurements can however lead to Bell nonlocality, as there exist incompatible sets of measurements which can only produce local correlations. In this Letter we prove that all sets of incompatible measurements are nevertheless able to generate nonlocality in an extended Bell scenario where quantum, instead of classical, measurement inputs are considered. In particular, this holds true for all incompatible-local sets of measurements and, consequently, shows that these sets of measurements posses a form of hidden nonlocality which can be revealed in such a scenario. We furthermore prove that the maximum amount of nonlocality that can be extracted in such a way is limited by the degree of incompatibility of the given set of measurements, thus effectively establishing an achievable upper bound. In order to obtain these results, we introduce a new object which we term a generalized set of measurements, which provides a unifying way to study any scenario involving quantum inputs.

Physical Review Letters•Mar 4, 2026•0 citations

All Incompatible Measurements on Qubits Lead to Multiparticle Bell Nonlocality

Martin Plávala, Otfried Gühne, Marco Túlio Quintino

Bell nonlocality is a fundamental phenomenon of quantum physics as well as an essential resource for various tasks in quantum information processing. It is known that for the observation of nonlocality the measurements on a quantum system have to be incompatible, but the question of which incompatible measurements are useful, remained open. Here we prove that any set of incompatible measurements on qubits leads to a violation of a suitable Bell inequality in a multiparticle scenario, where all parties perform the same set of measurements. Since there exists incompatible measurements on qubits which do not lead to Bell nonlocality for two particles, our results demonstrate a fundamental difference between two-particle and multiparticle nonlocality, pointing at the superactivation of measurement incompatibility as a resource. In addition, our results imply that measurement incompatibility for qubits can always be certified in a device-independent manner.

•Jan 1, 2025•0 citations

All incompatible sets of measurements can generate Buscemi nonlocality

Andrés F. Ducuara, Patryk Lipka-Bartosik, Cristian E. Susa +1 more

The presence of Bell-nonlocality in the correlations arising from measuring spatially-separated systems guarantees that the sets of measurements used are necessarily incompatible. Not all sets of incompatible measurements can however lead to Bell-nonlocality, as there exist incompatible sets of measurements which can only produce local correlations. In this work we prove that all sets of incompatible measurements are nevertheless able to generate nonlocality in an extended Bell scenario where quantum, instead of classical, measurement inputs are considered. In particular, this holds true for all incompatible-local sets of measurements and, consequently, shows that these sets of measurements posses a form of hidden nonlocality which can be revealed in such a scenario. We furthermore prove that the maximum amount of nonlocality that can be extracted in such a way is limited by the degree of incompatibility of the given set of measurements, thus effectively establishing an achievable upper bound. In order to obtain these results, we introduce a new object which we term a \emph{generalised set of measurements}, which provides a unifying way to study any scenario involving quantum inputs.

arXiv:2508.14421•Aug 20, 2025•0 citations

Incompatible quantum measurements admitting a local-hidden-variable model

Marco Túlio Quintino, Joseph Bowles, Flavien Hirsch +1 more

The observation of quantum nonlocality, i.e. quantum correlations violating a Bell inequality, implies the use of incompatible local quantum measurements. Here we consider the converse question. That is, can any set of incompatible measurements be used in order to demonstrate Bell inequality violation? Our main result is to construct a local hidden variable model for an incompatible set of qubit measurements. Specifically, we show that if Alice uses this set of measurements, then for any possible shared entangled state, and any possible dichotomic measurements performed by Bob, the resulting statistics are local. This represents significant progress towards proving that measurement incompatibility does not imply Bell nonlocality in general.

arXiv:1510.06722•Physical Review A•May 23, 2016•31 citations

Two important ingredients necessary for obtaining Bell nonlocal correlations between two spatially separated parties are an entangled state shared between them and an incompatible set of measurements employed by each of them. However, not all entangled states can give rise to Bell nonlocality. Here, we are interested in a complementary question, regarding the role of the sets of incompatible measurements in enabling Bell nonlocality, for arbitrary entangled states. It is known that for some sets of more than two jointly incompatible measurements performed by one of the parties, there does not exist an entangled state and another set of incompatible measurements for the other party, which will result in Bell nonlocality. However, in the two-input and two-output setting per party, measurement incompatibility at a single party will always guarantee Bell nonlocality. Thus, it is interesting to ask whether all sets of incompatible measurements at both parties, in the two-input and two-output setting per party, will result in Bell nonlocality for some shared state. We first observe that Bell nonlocality can always be established when both parties employ any set of incompatible projective measurements. On the other hand, going beyond projective measurements, we present a class of incompatible positive operator-valued measures, employed by both observers, which can never activate Bell nonlocality. Furthermore, we find a sufficient criterion for achieving Bell nonlocal correlations given a fixed amount of pure two-qubit entanglement and a fixed amount of incompatibility of projective measurements applied by either both parties or a single party.

We discuss the connection between the incompatibility of quantum measurements, as captured by the notion of joint measurability, and the violation of Bell inequalities. Specifically, we explicitly present a given set of non-jointly-measurable positive-operator-value measures (POVMs)

{\mathcal{M}}_{A}

with the following property. Considering a bipartite Bell test where Alice uses

{\mathcal{M}}_{A}

, then for any possible shared entangled state $\ensuremath{\rho}$ and any set of (possibly infinitely many) POVMs

{\mathcal{N}}_{B}

performed by Bob, the resulting statistics admits a local model and can thus never violate any Bell inequality. This shows that quantum measurement incompatibility does not imply Bell nonlocality in general.

Bell nonlocality is a fundamental phenomenon of quantum physics as well as an essential resource for various tasks in quantum information processing. It is known that for the observation of nonlocality the measurements on a quantum system have to be incompatible, but the question of which incompatible measurements are useful, remained open. Here we prove that any set of incompatible measurements on qubits leads to a violation of a suitable Bell inequality in a multiparticle scenario, where all parties perform the same set of measurements. Since there exists incompatible measurements on qubits which do not lead to Bell nonlocality for two particles, our results demonstrate a fundamental difference between two-particle and multiparticle nonlocality, pointing at the superactivation of measurement incompatibility as a resource. In addition, our results imply that measurement incompatibility for qubits can always be certified in a device-independent manner.

The presence of Bell nonlocality in the correlations arising from measuring spatially separated systems guarantees that the sets of measurements used are necessarily incompatible. Not all sets of incompatible measurements can however lead to Bell nonlocality, as there exist incompatible sets of measurements which can only produce local correlations. In this Letter we prove that all sets of incompatible measurements are nevertheless able to generate nonlocality in an extended Bell scenario where quantum, instead of classical, measurement inputs are considered. In particular, this holds true for all incompatible-local sets of measurements and, consequently, shows that these sets of measurements posses a form of hidden nonlocality which can be revealed in such a scenario. We furthermore prove that the maximum amount of nonlocality that can be extracted in such a way is limited by the degree of incompatibility of the given set of measurements, thus effectively establishing an achievable upper bound. In order to obtain these results, we introduce a new object which we term a generalized set of measurements, which provides a unifying way to study any scenario involving quantum inputs.

Bell nonlocality is a fundamental phenomenon of quantum physics as well as an essential resource for various tasks in quantum information processing. It is known that for the observation of nonlocality the measurements on a quantum system have to be incompatible, but the question of which incompatible measurements are useful, remained open. Here we prove that any set of incompatible measurements on qubits leads to a violation of a suitable Bell inequality in a multiparticle scenario, where all parties perform the same set of measurements. Since there exists incompatible measurements on qubits which do not lead to Bell nonlocality for two particles, our results demonstrate a fundamental difference between two-particle and multiparticle nonlocality, pointing at the superactivation of measurement incompatibility as a resource. In addition, our results imply that measurement incompatibility for qubits can always be certified in a device-independent manner.

The presence of Bell-nonlocality in the correlations arising from measuring spatially-separated systems guarantees that the sets of measurements used are necessarily incompatible. Not all sets of incompatible measurements can however lead to Bell-nonlocality, as there exist incompatible sets of measurements which can only produce local correlations. In this work we prove that all sets of incompatible measurements are nevertheless able to generate nonlocality in an extended Bell scenario where quantum, instead of classical, measurement inputs are considered. In particular, this holds true for all incompatible-local sets of measurements and, consequently, shows that these sets of measurements posses a form of hidden nonlocality which can be revealed in such a scenario. We furthermore prove that the maximum amount of nonlocality that can be extracted in such a way is limited by the degree of incompatibility of the given set of measurements, thus effectively establishing an achievable upper bound. In order to obtain these results, we introduce a new object which we term a \emph{generalised set of measurements}, which provides a unifying way to study any scenario involving quantum inputs.

The observation of quantum nonlocality, i.e. quantum correlations violating a Bell inequality, implies the use of incompatible local quantum measurements. Here we consider the converse question. That is, can any set of incompatible measurements be used in order to demonstrate Bell inequality violation? Our main result is to construct a local hidden variable model for an incompatible set of qubit measurements. Specifically, we show that if Alice uses this set of measurements, then for any possible shared entangled state, and any possible dichotomic measurements performed by Bob, the resulting statistics are local. This represents significant progress towards proving that measurement incompatibility does not imply Bell nonlocality in general.