Formulation of Leggett—Garg Inequalities in Terms of q-Entropies

Abstract

As is well known, the macroscopic realism and the noninvasive measurability together lead to Leggett—Garg inequalities violated by quantum mechanics. We consider tests of the Leggett—Garg type with use of the q-entropies. For all q ≥ 1, quantum mechanics predicts violations of an entire family of q-entropic inequalities of the Leggett—Garg type. Violations are exemplified with a quantum spin-s system. In general, entropic Leggett—Garg inequalities give only necessary conditions that some probabilistic model is compatible with the macrorealism in the broader sense. The presented q-entropic inequalities allow to widen a class of situations, in which an incompatibility with the macrorealism can be tested. In the considered example, both the strength and range of violations are somehow improved by varying q. We also examine q-entropic inequalities of the Leggett—Garg type in the case of detection inefficiencies, when the no-click event may occur in each observation. With the use of the q-entropic inequalities, the required amount of efficiency may be reduced.