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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.…
Bell inequalities are important tools in contrasting classical and quantum behaviors. To date, most Bell inequalities are linear combinations of statistical correlations between remote parties. Nevertheless, finding the classical and…
We investigate the maximal violation of Bell inequalities for two $d$-dimensional systems by using the method of Bell operator. The maximal violation corresponds to the maximal eigenvalue of the Bell operator matrix. The eigenvectors…
The Bell inequality constrains the outcomes of measurements on pairs of distant entangled particles. The Bell contradiction states that the Bell inequality is inconsistent with the calculated outcomes of these quantum experiments. This…
Standard multiparty Bell experiments involve a single source shared by a set of observers. In contrast, network Bell experiments feature multiple independent sources, and each of them may distribute physical systems to a set of observers…
For two qubits belonging to Alice and Bob, we derive an approach to setup the bound of Bell operator in the condition that Alice and Bob continue to perform local vertical measurements. For pure states we find that if the entanglement of…
In most Bell tests, the measurement settings are specially chosen so that the maximal quantum violations of the Bell inequalities can be detected, or at least, the violations are strong enough to be observed. Such choices can usually…
A Bell inequality is a constraint on a set of correlations whose violation can be used to certify non-locality. They are instrumental for device-independent tasks such as key distribution or randomness expansion. In this work we consider…
The no-signalling principle is a fundamental assumption in Bell-inequality and quantum-steering experiments. Nonetheless, experimental imperfections can lead to apparent violations beyond those expected from finite-sample statistics. Here,…
The worst violation of Bell's inequality for $n$ qbits is of size $2^{\frac{n-1}{2}}$ and it is obtained by a specific operator acting on a specific state. We show, to the contrary, that for a vast majority of Bell operators the worst…
Imperfect detection efficiency remains one of the major obstacles in achieving loophole-free Bell tests over long distances. At the same time, the challenge of establishing a common reference frame for measurements becomes more pronounced…
Bell's inequality sets a strict threshold for how strongly correlated the outcomes of measurements on two or more particles can be, if the outcomes of each measurement are independent of actions undertaken at arbitrarily distant locations.…
Bell-type inequalities and violations thereof reveal the fundamental differences between standard probability theory and its quantum counterpart. In the course of previous investigations ultimate bounds on quantum mechanical violations have…
The difference between ideal experiments to test Bell's weak nonlocality and the real experiments leads to loopholes. Ideal experiments involve either inequalities (Bell) or equalities (Greenberger, Horne, Zeilinger). Every real experiment…
In device-independent quantum information processing Bell inequalities are not only used as detectors of nonlocality, but also as certificates of relevant quantum properties. In order for these certificates to work, one very often needs…
The boundary between classical and quantum correlations is well characterised by linear constraints called Bell inequalities. It is much harder to characterise the boundary of the quantum set itself in the space of no-signaling…
Bell tests---the experimental demonstration of a Bell inequality violation---are central to understanding the foundations of quantum mechanics, underpin quantum technologies, and are a powerful diagnostic tool for technological developments…
Why do correlations between the results of measurements performed on physical systems violate Bell and non-contextuality inequalities up to some specific limits? The answer may follow from the observation that in quantum theory, unlike in…
Over the past few decades, experimental tests of Bell-type inequalities have been at the forefront of understanding quantum mechanics and its implications. These strong bounds on specific measurements on a physical system originate from…
It is not generally known, that the inequality that Bell derived using three random variables must be identically satisfied by any three corresponding data sets of plus and minus 1s that are writable on paper.This surprising fact is not…