Decoherence and maximal violations of the Leggett-Garg inequality

TL;DR

This paper investigates how environmental decoherence affects the maximum possible violations of the Leggett-Garg inequality in qubits, revealing thresholds where violations cease due to decoherence.

Contribution

It establishes a connection between quantum channel parameters and maximal Leggett-Garg violations, providing exact relations and identifying decoherence thresholds for violation.

Findings

Maximal violations depend on channel parameters.

Existence of thresholds below which violations do not occur.

Exact relations for unital channels and decoherence effects.

Abstract

We consider maximal violations of the Leggett-Garg inequality, obtained by maximising over all possible measurement operators, in relation to non-unitary aspects of the system dynamics. We model the action of an environment on a qubit in terms of generic quantum channels and relate the maximal value of the Leggett-Garg correlator to the channel parameters. We focus on unital channels, and hence on decoherence. In certain important cases, exact relations between the channel parameters and maximal violations can be found. Moreover, we demonstrate the existence of distinct thresholds for the channel parameters, below which no violation of the Leggett-Garg inequality can occur.