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Bell inequalities or Bell-like experiments are supposed to test hidden variable theories based on three intuitive assumptions: determinism, locality and measurement independence. If one of the assumptions of Bell inequality is properly…
In Bell scenario, any nonlocal correlation, shared between two spatially separated parties, can be modeled deterministically either by allowing communications between the two parties or by restricting their free will in choosing the…
The derivation of Bell inequalities requires an assumption of measurement independence, related to the amount of free will experimenters have in choosing measurement settings. Violation of these inequalities by singlet state correlations,…
The experimental violation of Bell inequality establishes necessary but not sufficient conditions that any theory must obey. Namely, a theory compatible with the experimental observations can satisfy at most two of the three hypotheses at…
A hidden variable model reproducing the quantum mechanical probabilities for a spin singlet is presented. The model violates only the hypothesis of independence of the distribution for the hidden variables from the detectors settings and…
If nonlocality is to be inferred from a violation of Bell's inequality, an important assumption is that the measurement settings are freely chosen by the observers, or alternatively, that they are random and uncorrelated with the…
Bell's seminal work showed that no local hidden variable (LHV) model can fully reproduce the quantum correlations of a two-qubit singlet state. His argument and later developments by Clauser et al. effectively rely on gaps between the…
Recent work has extended Bell's theorem by quantifying the amount of communication required to simulate entangled quantum systems with classical information. The general scenario is that a bipartite measurement is given from a set of…
The demonstration and use of Bell-nonlocality, a concept that is fundamentally striking and is at the core of applications in device independent quantum information processing, relies heavily on the assumption of measurement independence,…
A local hidden variable model exploiting the detection loophole to reproduce exactly the quantum correlation of the singlet state is presented. The model is shown to be compatible with both the CHSH and the CH Bell inequalities. Moreover,…
In a Bell experiment two parties share a quantum state and perform local measurements on their subsystems separately, and the statistics of the measurement outcomes are recorded as a Bell correlation. For any Bell correlation, it turns out…
In device-independent quantum information, correlations between local measurement outcomes observed by spatially separated parties in a Bell test play a fundamental role. Even though it is long-known that the set of correlations allowed in…
It is known that quantum correlations exhibited by a maximally entangled qubit pair can be simulated with the help of shared randomness, supplemented with additional resources, such as communication, post-selection or non-local boxes. For…
The Bell inequality is thought to be a common constraint shared by all models of local hidden variables that aim to describe the entangled states of two qubits. Since the inequality is violated by the quantum mechanical description of these…
The use of Bell's theorem in any application or experiment relies on the assumption of free choice or, more precisely, measurement independence, meaning that the measurements can be chosen freely. Here, we prove that even in the simplest…
Bell's theorem is often said to imply that quantum mechanics violates local causality, and that local causality cannot be restored with a hidden-variables theory. This however is only correct if the hidden-variables theory fulfils an…
Experimental tests of Bell's inequality allow to distinguish quantum mechanics from local hidden variable theories. Such tests are performed by measuring correlations of two entangled particles (e.g. polarization of photons or spins of…
A local and deterministic model of quantum correlations is always possible, as shown explicitly by Brans in 1988: one simply needs the physical systems being measured to have a suitable statistical correlation with the physical systems…
The combination of various physically plausible properties, such as no signaling, determinism, and experimental free will, is known to be incompatible with quantum correlations. Hence, these properties must be individually or jointly…
Determinism, no signaling and measurement independence are some of the constraints required for framing Bell inequality. Any model simulating nonlocal correlations must either individually or jointly give up these constraints. Recently M.…