Related papers: Perfect correlations between noncommuting observab…
It is well known that, in the description of quantum observables, positive operator valued measures (POVMs) generalize projection valued measures (PVMs) and they also turn out be more optimal in many tasks. We show that a commutative POVM…
We discuss the distinction between the notion of partial observable and the notion of complete observable. Mixing up the two is frequently a source of confusion. The distinction bears on several issues related to observability, such as (i)…
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…
We present a significantly improved scheme of entanglement detection inspired by local uncertainty relations for a system consisting of two qubits. Developing the underlying idea of local uncertainty relations, namely correlations, we…
In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be…
We reduce the question whether a given quantum mixed state is separable or entangled to the problem of existence of a certain full family of commuting normal matrices whose matrix elements are partially determined by components of the pure…
We introduce a new way of quantifying the degrees of incompatibility of two ob- servables in a probabilistic physical theory and, based on this, a global measure of the degree of incompatibility inherent in such theories, across all…
A new criterion, based on noncontextuality, is derived to discriminate between separable and nonseparable states in classical wave optics where no discreteness is involved. An experiment is proposed to test the violation of noncontextuality…
The paper is to prove the Gaussian correlation conjecture stating that, under the standard Gaussian measure, the measure of the intersection of any two symmetric convex sets is greater than or equal to the product of their measures.…
Reality of quantum observables, a feature of long-standing interest within foundations of quantum mechanics, has recently been quantified and deeply studied by means of entropic measures [Phys. Rev. A 97, 022107 (2018)]. However, there is…
In the paper, we devote to defining an available measure to quantify the nonbilocal correlation in the entanglement-swapping experiment. Then we obtain analytical formulas to calculate the quantifier when the inputs are pure states. For the…
The problem of the experimental determination of the amount of entanglement of a bipartite pure state is addressed. We show that measuring a single observable does not suffice to determine the entanglement of a given unknown pure state of…
We introduce an algebraic measure of correlations in bipartite quantum systems. The proposed quantity, called maximal mutual correlation, provides the information how much a given state differs from the product state of its marginals. In…
Universally valid uncertainty relations are proven in a model independent formulation for inherent and unavoidable extra noises in arbitrary joint measurements on single systems, from which Heisenber's original uncertainty relation is…
Complementarity restricts the accuracy with which incompatible quantum observables can be jointly measured. Despite popular conception, the Heisenberg uncertainty relation does not quantify this principle. We report the experimental…
Incompatibility of quantum measurements is of fundamental importance in quantum mechanics. It is closely related to many nonclassical phenomena such as Bell nonlocality, quantum uncertainty relations, and quantum steering. We study the…
A pair of quantum observables diagonal in the same "incoherent" basis can be measured jointly, so some coherence is obviously required for measurement incompatibility. Here we first observe that coherence in a single observable is linked to…
One of the most intriguing aspects of Quantum Mechanics is the impossibility of measuring at the same time observables corresponding to non-commuting operators. This impossibility can be partially relaxed when considering joint or…
In quantum theory, it is known for a pair of noncommutative observables that there is no state on which they take simultaneously definite values, and that there is no joint measurement of them. They are called preparation uncertainty and…
Coherence and correlations represent two related properties of a compound system. The system can be, for instance, the polarization of a photon, which forms part of a polarization-entangled two-photon state, or the spatial shape of a…