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We introduce Bell inequalities based on covariance, one of the most common measures of correlation. Explicit examples are discussed, and violations in quantum theory are demonstrated. A crucial feature of these covariance Bell inequalities…

Quantum Physics · Physics 2017-12-27 Victor Pozsgay , Flavien Hirsch , Cyril Branciard , Nicolas Brunner

Reichenbach's principle asserts that if two observed variables are found to be correlated, then there should be a causal explanation of these correlations. Furthermore, if the explanation is in terms of a common cause, then the conditional…

Information causality was initially proposed as a physical principle aimed at deriving the predictions of quantum mechanics on the type of correlations observed in the Bell experiment. In the same work, information causality was famously…

Quantum Physics · Physics 2024-11-08 Prabhav Jain , Mariami Gachechiladze , Nikolai Miklin

J.S. Bell's work has convinced many that correlations in violation of CHSH inequalities show that the world itself is non-local, and that there is an apparently essential conflict between any sharp formulation of quantum theory and…

Quantum Physics · Physics 2012-08-01 Richard Healey

Variational methods have proven to be excellent tools to approximate ground states of complex many body Hamiltonians. Generic tools like neural networks are extremely powerful, but their parameters are not necessarily physically motivated.…

Strongly Correlated Electrons · Physics 2022-03-04 Agnes Valenti , Eliska Greplova , Netanel H. Lindner , Sebastian D. Huber

Since Bell's theorem, it is known that quantum correlations cannot be described by local variables (LV) alone: if one does not want to abandon classical mechanisms for correlations, a superluminal form of communication among the particles…

Quantum Physics · Physics 2007-05-23 Valerio Scarani , Nicolas Gisin

We propose a method to generate analytical quantum Bell inequalities based on the principle of Macroscopic Locality. By imposing locality over binary processings of virtual macroscopic intensities, we establish a correspondence between Bell…

Quantum Physics · Physics 2011-02-17 Tzyh Haur Yang , Miguel Navascués , Lana Sheridan , Valerio Scarani

A problem in quantum information theory is to find the experimental setup that maximizes the nonlocality of correlations with respect to some suitable measure such as the violation of Bell inequalities. The latter has however some…

Quantum Physics · Physics 2016-08-30 Sacha Schwarz , Andre Stefanov , Stefan Wolf , Alberto Montina

We introduce the notion of empirical coordination for quantum correlations. Quantum mechanics enables the calculation of probabilities for experimental outcomes, emphasizing statistical averages rather than detailed descriptions of…

Quantum Physics · Physics 2025-04-08 Husein Natur , Uzi Pereg

The experimental violation of Bell inequalities using spacelike separated measurements precludes the explanation of quantum correlations through causal influences propagating at subluminal speed. Yet, any such experimental violation could…

Bell's theorem guarantees that no model based on local variables can reproduce quantum correlations. Also some models based on non-local variables, if subject to apparently "reasonable" constraints, may fail to reproduce quantum physics. In…

Bell's [Physics 1 (1964) 195-200] theorem is popularly supposed to establish the nonlocality of quantum physics. Violation of Bell's inequality in experiments such as that of Aspect, Dalibard and Roger [Phys. Rev. Lett. 49 (1982) 1804-1807]…

Applications · Statistics 2015-02-02 Richard D. Gill

Bell's theorem basically states that local hidden variable theory cannot predict the correlations produced by quantum mechanics. It is based on the assumption that Alice and Bob can choose measurements from a measurement set containing…

Quantum Physics · Physics 2011-11-22 Yang D. Li

Impossibility of finding local realistic models for quantum correlations due to entanglement is an important fact in foundations of quantum physics, gaining now new applications in quantum information theory. We present an in-depth…

Quantum Physics · Physics 2014-01-21 Jacek Gondzio , Jacek A. Gruca , J. A. Julian Hall , Wiesław Laskowski , Marek Żukowski

By assuming a deterministic evolution of quantum systems and taking realism into account, we carefully build a hidden variable theory for Quantum Mechanics based on the notion of ontological states proposed by 't Hooft. We view these…

Quantum Physics · Physics 2017-12-04 Natalia Sánchez-Kuntz , Eduardo Nahmad-Achar

Bell inequality violation is one of the most widely known manifestations of entanglement in quantum mechanics; indicating that experiments on physically separated quantum mechanical systems cannot be given a local realistic description.…

Quantum Physics · Physics 2007-05-23 Yeong-Cherng Liang , Andrew C. Doherty

It is well-known that in a Bell experiment, the observed correlation between measurement outcomes -- as predicted by quantum theory -- can be stronger than that allowed by local causality, yet not fully constrained by the principle of…

Quantum Physics · Physics 2022-07-15 Pei-Sheng Lin , Tamás Vértesi , Yeong-Cherng Liang

Generalizations of Bell's framework to causal networks have yielded new foundational insights and applications, including the use of interventions to enhance the detection of nonclassicality in scenarios with communication. Such…

Quantum Physics · Physics 2026-01-13 Santiago Zamora , Pedro Lauand , Isadora Veeren , Davide Poderini , Rafael Chaves

Understanding of how biological neural networks process information is one of the biggest open scientific questions of our time. Advances in machine learning and artificial neural networks have enabled the modeling of neuronal behavior, but…

Quantum Physics · Physics 2024-09-17 Vinicius Hernandes , Eliska Greplova

Bell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency. The assumption of a fixed causal order…

Quantum Physics · Physics 2016-04-06 Ämin Baumeler , Stefan Wolf