Related papers: Perfect correlations between noncommuting observab…
Joint or simultaneous measurements of non-commuting quantum observables are possible at the cost of increased unsharpness or measurement uncertainty. Many different criteria exist for defining what an "optimal" joint measurement is, with…
The aim of this paper is to study the probability that the commutator of an arbitrarily chosen pair of elements, each from two different subrings of a finite non-commutative ring equals a given element of that ring. We obtain several…
Quantum correlation includes quantum entanglement and quantum discord. Both entanglement and discord have a common necessary condition--------quantum coherence or quantum superposition. In this paper, we attempt to give an alternative…
The noncontextuality of quantum mechanics can be directly tested by measuring two entangled particles with more than two outcomes per particle. The two associated contexts are "interlinked" by common observables.
In terms of operator, the two complementary quantities, the predictability and visibility, are reinvestigated in a two-way interferometer. One Hermitian operator and one non-Hermitian operator (composed of two Hermitian operators) are…
We provide a consistency relation between cosmological observables in general relativity with the cosmological constant. Breaking of this relation at any redshift would imply the breakdown of the hypothesis of the cosmological constant as…
We derive quantitative relations among several naturally defined measures of classical and nonclassical correlations in a bipartite quantum state. We also obtain an upper bound of entanglement irreversibility and a sufficient condition for…
We review two general criteria for deciding whether a pure bipartite quantum state describing a system of two identical particles is entangled or not. The first one considers the possibility of attributing a complete set of objective…
We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in…
Based on the Pauli spin operators we develop the notion of the spin-correlation matrix for the two-qubit system. If this matrix is non-zero, the measure of the correlation between the qubits is the average of the non-zero elements.…
On the complete graph ${\cal{K}}_M$ with $M \ge3$ vertices consider two independent discrete time random walks $\mathbb{X}$ and $\mathbb{Y}$, choosing their steps uniformly at random. A pair of trajectories $\mathbb{X} = \{ X_1, X_2, \dots…
We intend to eliminate the known conflict between relativity and quantum mechanics. We believe the instant correlation between entangled distant quantum particles can be explained by the fact that in a laboratory reference frame the photon…
We begin by defining mutually unbiased (MU) observables on a finite dimensional Hilbert space. We also consider the more general concept of parts of MU observables. The relationships between MU observables, value-complementary observables…
In this article, we revisit the century-old question of the minimal set of observables needed to identify a quantum state: here, we replace the natural coincidences in their spectra by effective ones, induced by an imperfect measurement. We…
We provide an in-depth study of the recently introduced notion of completely incompatible observables and its links to the support uncertainty and to the Kirkwood-Dirac nonclassicality of pure quantum states. The latter notion has recently…
We investigate the interplay and connections between symmetry properties of equations, the interpretation of coordinates, the construction of observables, and the existence of physical relativity principles in spacetime theories. Using the…
We study the local indistinguishability problem of quantum states. By introducing an easily calculated quantity, non-commutativity, we present an criterion which is both necessary and sufficient for the local indistinguishability of a…
Entanglement, which is an essential characteristic of quantum mechanics, is the key element in potential practical quantum information and quantum communication systems. However, there are many open and fundamental questions (relating to…
Generalized uncertainty relations may depend not only on the commutator relation of two observables considered, but also on mutual correlations, in particular, on entanglement. The equivalence between the uncertainty relation and Bohr's…
Quantum measurements are noncontextual, with outcomes independent of which other commuting observables are measured at the same time, when consistently analyzed using principles of Hilbert space quantum mechanics rather than classical…