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To maximize average information gain for a classical measurement, all outcomes of an observation must be equally likely. The condition of equally likely outcomes may be enforced in quantum theory by ensuring that one's state $\rho$ is…
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…
How well can multiple incompatible observables be implemented by a single measurement? This is a fundamental problem in quantum mechanics with wide implications for the performance optimization of numerous tasks in quantum information…
The standard Bell inequality experiments test for violation of local realism by repeatedly making local measurements on individual copies of an entangled quantum state. Here we investigate the possibility of increasing the violation of a…
We introduce a hierarchy of conditions necessarily satisfied by any distribution P(ab) representing the probabilities for two separate observers to obtain outcomes a and b when making local measurements on a shared quantum state. Each…
Quantum correlations described by quantum discord and one-way quantum deficit can contain ordinary regions with {\em constant} (i.e., universal) optimal measurement angle $0$ or $\pi/2$ with respect to the $z$-axis and regions with a {\em…
In the first part of this presentation (sections 2 to 6), I show that Bell's Inequalities provide a quantitative criterion to test "reasonable" Supplementary Parameters Theories versus Quantum Mechanics. Following Bell, I first explain the…
We present a family of Bell inequalities for three parties and arbitrarily many outcomes, which can be seen as a natural generalization of the Mermin Bell inequality. For a small number of outcomes, we verify that our inequalities define…
We review the status of Bell's inequalities in quantum information, stressing mainly the links with quantum key distribution and distillation of entanglement. We also prove that for all the eavesdropping attacks using one qubit, and for a…
A problem in quantum information theory is to find the experimental setup that maximizes the nonlocality of correlations with respect to some suitable measure such as the violation of Bell inequalities. The latter has however some…
We consider the problem of certifying measurement incompatibility in a prepare-and-measure (PM) scenario. We present different families of sets of qubit measurements which are incompatible, but cannot lead to any quantum over classical…
In Coles-Piani's recent remarkable version of the entropic uncertainty principle, the entropic sum is controlled by the first and second maximum overlaps between the two projective measurements. We generalize the entropic uncertainty…
Bell's inequalities are defined by sums of correlations involving non-commuting observables in each of the two systems. Violations of Bell's inequalities are only possible because the precision of any joint measurement of these observables…
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…
Complementarity is one of the main features of quantum physics that radically departs from classical notions. Here we consider the limitations that this principle imposes due to the unpredictability of measurement outcomes of incompatible…
So far, various Bell type inequalities have been introduced to test the local realism in tripartite systems. In this article we consider a tripartite system with two measurements in each side and two outputs for each measurement. Then we…
It is well known that the maximal violation of the Bell's inequality for a two-qubit system is related to the entanglement formation in terms of a concurrence. However, a generalization of this relation to an $n$-qubit state has not been…
We describe and realize an experimental procedure for assessing the incompatibility of two qubit measurements. The experiment consists in a state discrimination task where either measurement is used according to some partial intermediate…
Solid experimental evidence has now been obtained that confirms the violation of Bell's inequality in tests of maximally entangled qubit pairs. This violation is widely interpreted as definitive proof of the impossibility of describing…
The Bell inequalities in three and four correlations are re-derived in general forms showing that three and four data sets, respectively, identically satisfy them regardless of whether they are random, deterministic, measured, predicted, or…