Macrorealism from entropic Leggett-Garg inequalities

TL;DR

This paper introduces entropic Leggett-Garg inequalities to test macrorealism, demonstrating their violation by quantum spin systems, similar to entropic Bell inequalities, thus providing a new information-theoretic approach to quantum temporal correlations.

Contribution

It formulates entropic Leggett-Garg inequalities and shows their violation by quantum spin systems, linking temporal quantum correlations with spatial entanglement concepts.

Findings

Entropic Leggett-Garg inequalities are satisfied by macrorealist theories.

Quantum spin systems violate these inequalities, indicating non-classical temporal correlations.

Violation parallels that of entropic Bell inequalities in spatially separated systems.

Abstract

We formulate entropic Leggett-Garg inequalities, which place constraints on the statistical outcomes of temporal correlations of observables. The information theoretic inequalities are satisfied if macrorealism holds. We show that the quantum statistics underlying correlations between time-separated spin component of a quantum rotor mimics that of spin correlations in two spatially separated spin-$s$ particles sharing a state of zero total spin. This brings forth the violation of the entropic Leggett-Garg inequality by a rotating quantum spin-$s$ system in similar manner as does the entropic Bell inequality (Phys. Rev. Lett. 61, 662 (1988)) by a pair of spin-$s$ particles forming a composite spin singlet state.