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:0910.3952 · Physical Review Letters

Local Quantum Measurement and No-Signaling Imply Quantum Correlations

Howard Barnum, Salman Beigi, Sergio Boixo, Matthew Elliott, Stephanie Wehner

Published Apr 6, 2010• 147 citations
arXivHTMLPDF

Abstract

We show that, assuming that quantum mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. Local quantum mechanics means that a Hilbert space is assigned to each party, and then all local positive-operator-valued measurements are (in principle) available; however, the joint system is not necessarily described by a Hilbert space. In particular, we do not assume the tensor product formalism between the joint systems. Our result shows that if any experiment would give nonlocal correlations beyond quantum mechanics, quantum theory would be invalidated even locally.

DOI
10.1103/physrevlett.104.140401

Related papers

JOINT SYSTEM QUANTUM DESCRIPTIONS ARISING FROM LOCAL QUANTUMNESS

Tom Cooney, Marius Junge, Miguel Navascués +2 more

Bipartite correlations generated by non-signalling physical systems that admit a finite-dimensional local quantum description cannot exceed the quantum limits, i.e., they can always be interpreted as distant measurements of a bipartite quantum state. Here we consider the effect of dropping the assumption of finite dimensionality. Remarkably, we find that the same result holds provided that we relax the tensor structure of space-like separated measurements to mere commutativity. We argue why an extension of this result to tensor representations seems unlikely.

•Jan 1, 2013•1 citation

Exploring the local orthogonality principle

Ana Belén Sainz, T. Fritz, Remigiusz Augusiak +4 more

Nonlocality is arguably one of the most fundamental and counterintuitive aspects of quantum theory. Nonlocal correlations could, however, be even more nonlocal than quantum theory allows, while still complying with basic physical principles such as no-signaling. So why is quantum mechanics not as nonlocal as it could be? Are there other physical or information-theoretic principles which prohibit this? So far, the proposed answers to this question have been only partially successful, partly because they are lacking genuinely multipartite formulations. In Fritz et al. [Nat. Commun. 4, 2263 (2013)], we introduced the principle of local orthogonality (LO), an intrinsically multipartite principle which is satisfied by quantum mechanics but is violated by nonphysical correlations. Here we further explore the LO principle, presenting additional results and explaining some of its subtleties. In particular, we show that the set of no-signaling boxes satisfying LO is closed under wirings, present a classification of all LO inequalities in certain scenarios, show that all extremal tripartite boxes with two binary measurements per party violate LO, and explain the connection between LO inequalities and unextendible product bases.

arXiv:1311.6699•Physical Review A•Mar 13, 2014•46 citations

Local measurement uncertainties impose a limit on nonlocal quantum correlations

Holger Friedrich Hofmann

In quantum mechanics, joint measurements of noncommuting observables are only possible if a minimal unavoidable measurement uncertainty is accepted. On the other hand, correlations between noncommuting observables can exceed classical limits, as demonstrated by the violation of Bell's inequalities. Here, the relation between the uncertainty-limited statistics of joint measurements and the limits on expectation values of possible input states is analyzed. It is shown that the experimentally observable statistics of joint measurements explain the uncertainty limits of local states, but result in less restrictive bounds when applied to identify the limits of nonlocal correlations between two separate quantum systems. A tight upper bound is obtained for the four correlations that appear in the violation of Bell's inequalities and the statistics of pure states saturating the bound is characterized. The results indicate that the limitations of quantum nonlocality are a necessary consequence of the local features of joint measurements, suggesting the possibility that quantum nonlocality could be explained in terms of the local characteristics of quantum statistics.

arXiv:1809.04725•Physical Review A•Jul 22, 2019•14 citations

Computability limits nonlocal correlations

Tanvirul Islam, Stephanie Wehner

If the no-signaling principle was the only limit to the strength of nonlocal correlations, we would expect that any form of no-signaling correlation can indeed be realized. That is, there exists a state and measurements that remote parties can implement to obtain any such correlation. Here, we show that in any theory in which some functions cannot be computed, there must be further limits to nonlocal correlations than the no-signaling principle alone. We proceed to argue that even in a theory such as quantum mechanics in which nonlocal correlations are already weaker, the question of computability imposes such limits.

arXiv:1205.1288•Physical Review A•Oct 10, 2012•3 citations

LOCAL CAUSALITY AND THE FOUNDATIONS OF QUANTUM MECHANICS

Robert S. Goldstein

Quantum mechanics implies the existence of correlations which cannot be described by any local theory. These nonlocal correlations possibly suggest the existence of particles traveling faster than light (tachyons). But the potential paradoxes associated with their existence imply that, even i f these tachyons do exist, it should not be possible to control them in a manner necessary for human superluminal (faster than light) communication. Indeed, the unitary nature of the time development operator precludes the possibility of using non-local correlations to communicate superluminally within the quantum formalism. A simplified model which preserves unitary time development i s shown to be useful in studying 'thought experiments' which appear init ially to allow for superluminal communication. The consistency of quantum mechanics is questioned when measurements of retarded fields are considered. I f certain idealized measurements are possible in principle, then the quantum formalism appears inconsistent. I f the measurements are not possible in principle, then 'state reduct ion' (non-unitary time evolution of the state operator) in a pragmatic sense can be said to have occurred. The suggestion that tachyons be used to explain the non-local correlations i s abandoned in favor of another model whose philosophy is supported by the tenets of relativity theory. Such a model may imply the existence of a more general quantum theory where a quantum system itself can be taken as a (generalized) frame of reference.

•Jan 1, 1987•0 citations

Limits on nonlocal correlations from the structure of the local state space

Peter Janotta, Christian Gogolin, Jonathan Barrett +1 more

The outcomes of measurements on entangled quantum systems can be nonlocally correlated. However, while it is easy to write down toy theories allowing arbitrary nonlocal correlations, those allowed in quantum mechanics are limited. Quantum correlations cannot, for example, violate a principle known as macroscopic locality, which implies that they cannot violate Tsirelson's bound. This paper shows that there is a connection between the strength of nonlocal correlations in a physical theory and the structure of the state spaces of individual systems. This is illustrated by a family of models in which local state spaces are regular polygons, where a natural analogue of a maximally entangled state of two systems exists. We characterize the nonlocal correlations obtainable from such states. The family allows us to study the transition between classical, quantum and super-quantum correlations by varying only the local state space. We show that the strength of nonlocal correlations—in particular whether the maximally entangled state violates Tsirelson's bound or not—depends crucially on a simple geometric property of the local state space, known as strong self-duality. This result is seen to be a special case of a general theorem, which states that a broad class of entangled states in probabilistic theories—including, by extension, all bipartite classical and quantum states—cannot violate macroscopic locality. Finally, our results show that models exist that are locally almost indistinguishable from quantum mechanics, but can nevertheless generate maximally nonlocal correlations.

arXiv:1012.1215•New Journal of Physics•Jun 14, 2011•91 citations
We show that, assuming that quantum mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. Local quantum mechanics means that a Hilbert space is assigned to each party, and then all local positive-operator-valued measurements are (in principle) available; however, the joint system is not necessarily described by a Hilbert space. In particular, we do not assume the tensor product formalism between the joint systems. Our result shows that if any experiment would give nonlocal correlations beyond quantum mechanics, quantum theory would be invalidated even locally.
Bipartite correlations generated by non-signalling physical systems that admit a finite-dimensional local quantum description cannot exceed the quantum limits, i.e., they can always be interpreted as distant measurements of a bipartite quantum state. Here we consider the effect of dropping the assumption of finite dimensionality. Remarkably, we find that the same result holds provided that we relax the tensor structure of space-like separated measurements to mere commutativity. We argue why an extension of this result to tensor representations seems unlikely.
Nonlocality is arguably one of the most fundamental and counterintuitive aspects of quantum theory. Nonlocal correlations could, however, be even more nonlocal than quantum theory allows, while still complying with basic physical principles such as no-signaling. So why is quantum mechanics not as nonlocal as it could be? Are there other physical or information-theoretic principles which prohibit this? So far, the proposed answers to this question have been only partially successful, partly because they are lacking genuinely multipartite formulations. In Fritz et al. [Nat. Commun. 4, 2263 (2013)], we introduced the principle of local orthogonality (LO), an intrinsically multipartite principle which is satisfied by quantum mechanics but is violated by nonphysical correlations. Here we further explore the LO principle, presenting additional results and explaining some of its subtleties. In particular, we show that the set of no-signaling boxes satisfying LO is closed under wirings, present a classification of all LO inequalities in certain scenarios, show that all extremal tripartite boxes with two binary measurements per party violate LO, and explain the connection between LO inequalities and unextendible product bases.
In quantum mechanics, joint measurements of noncommuting observables are only possible if a minimal unavoidable measurement uncertainty is accepted. On the other hand, correlations between noncommuting observables can exceed classical limits, as demonstrated by the violation of Bell's inequalities. Here, the relation between the uncertainty-limited statistics of joint measurements and the limits on expectation values of possible input states is analyzed. It is shown that the experimentally observable statistics of joint measurements explain the uncertainty limits of local states, but result in less restrictive bounds when applied to identify the limits of nonlocal correlations between two separate quantum systems. A tight upper bound is obtained for the four correlations that appear in the violation of Bell's inequalities and the statistics of pure states saturating the bound is characterized. The results indicate that the limitations of quantum nonlocality are a necessary consequence of the local features of joint measurements, suggesting the possibility that quantum nonlocality could be explained in terms of the local characteristics of quantum statistics.
If the no-signaling principle was the only limit to the strength of nonlocal correlations, we would expect that any form of no-signaling correlation can indeed be realized. That is, there exists a state and measurements that remote parties can implement to obtain any such correlation. Here, we show that in any theory in which some functions cannot be computed, there must be further limits to nonlocal correlations than the no-signaling principle alone. We proceed to argue that even in a theory such as quantum mechanics in which nonlocal correlations are already weaker, the question of computability imposes such limits.
Quantum mechanics implies the existence of correlations which cannot be described by any local theory. These nonlocal correlations possibly suggest the existence of particles traveling faster than light (tachyons). But the potential paradoxes associated with their existence imply that, even i f these tachyons do exist, it should not be possible to control them in a manner necessary for human superluminal (faster than light) communication. Indeed, the unitary nature of the time development operator precludes the possibility of using non-local correlations to communicate superluminally within the quantum formalism. A simplified model which preserves unitary time development i s shown to be useful in studying 'thought experiments' which appear init ially to allow for superluminal communication. The consistency of quantum mechanics is questioned when measurements of retarded fields are considered. I f certain idealized measurements are possible in principle, then the quantum formalism appears inconsistent. I f the measurements are not possible in principle, then 'state reduct ion' (non-unitary time evolution of the state operator) in a pragmatic sense can be said to have occurred. The suggestion that tachyons be used to explain the non-local correlations i s abandoned in favor of another model whose philosophy is supported by the tenets of relativity theory. Such a model may imply the existence of a more general quantum theory where a quantum system itself can be taken as a (generalized) frame of reference.
The outcomes of measurements on entangled quantum systems can be nonlocally correlated. However, while it is easy to write down toy theories allowing arbitrary nonlocal correlations, those allowed in quantum mechanics are limited. Quantum correlations cannot, for example, violate a principle known as macroscopic locality, which implies that they cannot violate Tsirelson's bound. This paper shows that there is a connection between the strength of nonlocal correlations in a physical theory and the structure of the state spaces of individual systems. This is illustrated by a family of models in which local state spaces are regular polygons, where a natural analogue of a maximally entangled state of two systems exists. We characterize the nonlocal correlations obtainable from such states. The family allows us to study the transition between classical, quantum and super-quantum correlations by varying only the local state space. We show that the strength of nonlocal correlations—in particular whether the maximally entangled state violates Tsirelson's bound or not—depends crucially on a simple geometric property of the local state space, known as strong self-duality. This result is seen to be a special case of a general theorem, which states that a broad class of entangled states in probabilistic theories—including, by extension, all bipartite classical and quantum states—cannot violate macroscopic locality. Finally, our results show that models exist that are locally almost indistinguishable from quantum mechanics, but can nevertheless generate maximally nonlocal correlations.