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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…

Local realism in recent experiments is excluded on condition of freedom or randomness of choice combined with no signaling between observers by implementations of simple quantum models. Both no-signaling and the underlying quantum model can…

Does determinism (or even the incompleteness of quantum mechanics) follow from locality and perfect correlations? In a 1964 paper John Bell gave the first demonstration that quantum mechanics is incompatible with local hidden variables.…

Bell's theorem of 1965 is a proof that all realistic interpretations of quantum mechanics must be non-local. Bell's theorem consists of two parts: first a correlation inequality is derived that must be satisfied by all local realistic…

The number of steps required in order to maximize a Bell inequality for arbitrary number of qubits is shown to grow exponentially with either the number of steps and the number of parties involved. The proof that the optimization of such…

We expand the scope of the statistical notion of error probability, i.e., how often large deviations are observed in an experiment, in order to make it directly applicable to quantum tomography. We verify that the error probability can…

Understanding the connections between different quantum information protocols has been proven fruitful for both theoretical insights and experimental applications. In this work, we explore the relationship between non-local and…

Randomization inference is a widely-used and appealing approach for analyzing treatment effects in randomized experiments, as it is finite-sample valid and does not require any distributional assumptions. However, naive application of…

Measurements of quantum states form a key component in quantum-information processing. It is therefore an important task to compare measurements and furthermore decide if a measurement strategy is optimal. Entropic quantities, such as the…

Bell's theorem rests on the following fundamental condition for a local system: P(a,b|alpha, beta, lambda)= P(a|alpha, lambda)P(b|beta, lambda). Here a and b are the outcomes respectively for measurements alpha on one side, and beta on the…

We consider the expected violations of Bell inequalities from random pure states. More precisely, we focus on a slightly generalised version of the CGLMP inequality, which concerns Bell experiments of two parties, two measurement options…

We introduce a permutationally invariant multipartite Bell inequality for many-body three-level systems and use it to investigate a connection between Bell nonlocality and (lack of) quantum chaos. An associated Bell operator is then defined…

It is well known that the effect of quantum nonlocality, as witnessed by violation of a Bell inequality, can be observed even when relaxing the assumption of measurement independence, i.e. allowing for the source to be partially correlated…

For more than 80 years, the counterintuitive predictions of quantum theory have stimulated debate about the nature of reality. In his seminal work, John Bell proved that no theory of nature that obeys locality and realism can reproduce all…

Chen (quant-ph/0611126) has recently claimed ``exponential violation of local realism by separable states", in the sense that multi-partite separable quantum states are supposed to give rise to correlations and fluctuations that violate a…

This article shows that the there is no paradox. Violation of Bell's inequalities should not be identified with a proof of non locality in quantum mechanics. A number of past experiments is reviewed, and it is concluded that the…

We study multipartite Bell nonlocality in a framework native of multipartite Einstein-Podolsky-Rosen (EPR) steering scenarios with a single trusted measurement device. We derive a closed-form necessary and sufficient criterion for systems…

Simple quantitative measures of indeterminism and signalling, $I$ and $S$, are defined for models of statistical correlations. It is shown that any such model satisfies a generalised Bell-type inequality, with tight upper bound B(I,S). This…

The failure of Bell's theorem for Clifford algebra valued local variables is further consolidated by proving that the conditions of remote parameter independence and remote outcome independence are duly respected within the recently…

For a multipartite quantum state, the maximal violation of all Bell inequalities constitutes a measure of its nonlocality [Loubenets, J. Math. Phys. 53, 022201 (2012)]. In the present article, for the maximal violation of Bell inequalities…