Wigner inequalities for testing the hypothesis of realism and concepts of macroscopic and local realism

Abstract

We propose a new Wigner inequality suitable for test of the hypothesis of realism. We show that this inequality is not identical neither to the well-known Wigner inequality nor to the Leggett-Garg inequality in Wigner form. The obtained inequality is suitable for test of realism not only in quantum mechanical systems, but also in quantum field systems.Also we propose a mathematically consistent derivation of the Leggett-Garg inequality in Wigner form, which was recently presented in the literature, for three and n distinct moments of time. Contrary to these works, our rigor derivation uses Kolmogorov axiomatics of probability theory. We pay special attention to the construction and studies of the spaces of elementary outcomes. Basing on the the Leggett-Garg inequality in Wigner form for n distinct moments of time we prove that any unitary evolution of a quantum system contradicts the concept of macroscopic realism. We show that application of the concept of macroscopic realism to any quantum system leads to "freezing" of the system in the initial state.It is shown that for a particle with an infinite number of observables the probability to find a pair of the observables in some defined state is zero, even if the operators of these observables commute. This fact might serve as an additional logical argument for the contradiction between quantum theory and classical realism.

Quantum discord and entropic measures of two relativistic fermions

“…The entropy of the spin part of A was found in Eq. (31). The relative entropy of the spin part of A follows the same type of partitioning 1 + 3 and is equal to…”

“…The concept of quantum correlations and entanglement is related to quantum coherence and measurements. Typically, measurements performed on a quantum system involve classical devices, and therefore the measurement setup exerts an unavoidable invasive effect on the coherence of the quantum state [24][25][26][27][28][29][30][31][32][33] . In order to explore the robustness of quantum discord with respect to measurements for a particle-antiparticle pair, we evaluate quantum discord after implementing a POVM.…”

Quantum discord and entropic measures of two relativistic fermions

“…The concept of quantum correlations and entanglement is related to quantum coherence and measurements. Typically, measurements performed on a quantum system involve classical devices, and therefore the measurement setup exerts an unavoidable invasive effect on the coherence of the quantum state [27][28][29][30][31][32][33][34][35][36]. In order to explore the robustness of quantum discord with respect to measurements for a particle-antiparticle pair, we evaluate quantum discord after implementing a POVM.…”

Quantum witness and invasiveness of cosmic neutrino measurements

“…It should be noted that the phenomenon of neutrino oscillations is closely related to the concept of quantum coherence. This concept touches upon the macroscopic coherence, i.e., superposition of a macroscopic large number of states and involves two core principles: (i) macroscopic realism per se argues that the pre-existing value of the quantity in question can be inferred through the measurements done on the macroscopic system, (ii) noninvasive measurability means that one can perform measurement without distorting the state of the system [18][19][20][21][22][23][24][25][26][27]. In reality the situation is more complex.…”