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Bell's theorem states that no local realistic explanation of quantum mechanical predictions is possible, in which the experimenter has a freedom to choose between different measurement settings. Within a local realistic picture the…

With the advent of quantum information, the violation of a Bell inequality is used as evidence of the absence of an eavesdropper in cryptographic scenarios such as key distribution and randomness expansion. One of the key assumptions of…

Certifying maximal quantum randomness without assumptions about system dimension remains a pivotal challenge for secure communication and foundational studies. Here, we introduce a generalized framework to directly certify maximal…

Bell inequalities rest on three fundamental assumptions: realism, locality, and free choice, which lead to nontrivial constraints on correlations in very simple experiments. If we retain realism, then violation of the inequalities implies…

Bell test is one of the most important tools in quantum information science. On the one hand, it enables fundamental test for the physics laws of nature, and on the other hand, it can be also applied in varieties of device independent tasks…

Device-independent randomness generation and quantum key distribution protocols rely on a fundamental relation between the non-locality of quantum theory and its random character. This relation is usually expressed in terms of a trade-off…

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.…

Self-testing--the attractive possibility to infer the underlying physics of a quantum device in a black-box scenario--has gained increased traction in recent years, with applications to device-independent quantum information processing.…

Bell's theorem is typically understood as the proof that quantum theory is incompatible with local-hidden-variable models. More generally, we can see the violation of a Bell inequality as witnessing the impossibility of explaining quantum…

Randomness is a fundamental feature in nature and a valuable resource for applications ranging from cryptography and gambling to numerical simulation of physical and biological systems. Random numbers, however, are difficult to characterize…

We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…

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…

A simple classical, deterministic, local situation violating the Bell inequality is described. The detectors used in the experiment are ideal and the observers who decide which pair of measuring devices to choose for a given pair of…

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 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…

The majority of recent works investigating the link between non-locality and randomness, e.g. in the context of device-independent cryptography, do so with respect to some specific Bell inequality, usually the CHSH inequality. However, the…

One of the striking properties of quantum mechanics is the occurrence of the Bell-type non-locality. They are a fundamental feature of the theory that allows two parties that share an entangled quantum system to observe correlations…

The violation of Bell inequality not only provides the most radical departure of quantum theory from classical concepts, but also paves the way of applications in such as device independent randomness certification. Here, we derive the…

The assumption of measurement independence is required for a local deterministic model to conduct a Bell test. The violation of a Bell inequality by such a model implies that this assumption must be relaxed. The degree to which the…

The detection of nonlocal correlations in a Bell experiment implies almost by definition some intrinsic randomness in the measurement outcomes. For given correlations, or for a given Bell violation, the amount of randomness predicted by…