Decoherence and maximal violations of the Leggett-Garg inequality

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.

7 pages; 3 figures

References in corpus (5)

• Distinguishing quantum and classical transport through nanostructures
• Leggett-Garg inequalities and the geometry of the cut polytope
• The Leggett-Garg inequality in electron interferometers
• Leggett-Garg inequalities for the statistics of electron transport
• Comment on `A scattering quantum circuit for measuring Bell's time inequality: a nuclear magnetic resonance demonstration using maximally mixed states'

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• Leggett-Garg inequality in Markovian quantum dynamics: role of temporal sequencing of coupling to bath
• Leggett-Garg inequalities for multitime processes