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Complementary relationships exist regarding interference properties of particles such as pattern visibility, predictability and distinguishability. Additionally, relationships are known between information gain $G$ and measurement…
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…
The two-particle correlation obtained from the quantum state used in the Bell inequality is sinusoidal, but the standard Bell inequality only uses two pairs of settings and not the whole sinusoidal curve. The highest to-date visibility of…
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 non-locality represents one of the most striking departures of quantum mechanics from classical physics. It shows that correlations between space-like separated systems allowed by quantum mechanics are stronger than those present in…
The violation of a Bell inequality is an experimental observation that forces one to abandon a local realistic worldview, namely, one in which physical properties are (probabilistically) defined prior to and independent of measurement and…
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.…
Measurements in quantum theory can fail to be jointly measurable. Like entanglement, this incompatibility of measurements is necessary but not sufficient for violating Bell inequalities. The (in)compatibility relations among a set of…
We examine the problem of exhibiting Bell nonlocality for a two-qudit entangled pure state using a randomly chosen set of mutually unbiased bases (MUBs). Interestingly, even if we employ only two-setting Bell inequalities, we find a…
We propose a class of incompatibility measures for quantum observables based on quantifying the effect of a measurement of one observable on the statistics of the outcomes of another. Specifically, for a pair of observables $A$ and $B$ with…
We consider the problem of certifying binary observables based on a Bell inequality violation alone, a task known as self-testing of measurements. We introduce a family of commutation-based measures, which encode all the distinct…
This is a review devoted to the complementarity-contextuality interplay with connection to the Bell inequalities. Starting discussion with complementarity, we point out to contextuality as its seed. {\it Bohr-contextuality} is dependence of…
We analyze conditions for violation of the Bell inequality in the Clauser-Horne-Shimony-Holt form, focusing on the Josephson phase qubits. We start the analysis with maximum violation in the ideal case, and then take into account the…
Last years, bounds on the maximal quantum violation of general Bell inequalities were intensively discussed in the literature via different mathematical tools. In the present paper, we analyze quantum violation of general Bell inequalities…
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…
Communication complexity problems (CCPs) are tasks in which separated parties attempt to compute a function whose inputs are distributed among the parties. Their communication is limited so that not all inputs can be sent. We show that…
We find a single parameter family of genuinely entangled three qubit pure states, called the maximally Bell inequality violating states (MBV), which exhibit maximum Bell inequality violation by the reduced bipartite system for a fixed…
Nonlocal tests on multi-partite quantum correlations form the basis of protocols that certify randomness in a device-independent (DI) way. Such correlations admit a rich structure, making the task of choosing an appropriate test difficult.…
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…
We present a generalized Bell inequality for two entangled quNits. On one quNit the choice is between two standard von Neumann measurements, whereas for the other quNit there are $N^2$ different binary measurements. These binary…