Canonical Leggett-Garg Inequality: Nonclassicality of temporal quantum correlations under energy constraint

TL;DR

This paper explores the energy costs and robustness of Leggett-Garg inequality violations in quantum systems under energy constraints and noise, revealing optimal conditions and environmental resilience.

Contribution

It introduces an energy-constrained framework for analyzing Leggett-Garg inequalities and demonstrates the conditions for maximal violation and robustness against noise.

Findings

Maximal LGI violation occurs when average energy equals negative initial energy.

LGI violations are robust under moderate Markovian noise with proper evolution choices.

Energy constraints influence the initial state dependence of LGI violations.

Abstract

Nonclassicality of temporal correlations pertaining to noncommutative sequential measurements is defined through the violation of macrorealistic inequalities, known as Leggett-Garg inequalities (LGI). We investigate the energy cost of the process associated with the Leggett-Garg test in the context of noiseless and Markovian noise for arbitrary initial states. We prove that in noiseless and in certain noisy scenarios, the maximal violations of LGI under the energy constraint occurs when the average energy of the process is equal to the negative of the energy of the initial state. Such a dependence of LGI on the choice of the initial state is not seen in the unconstrained case. Moreover, we find that in the presence of a moderate amount of Markovian noise, the amount of violation of LGI remains almost unaltered with a suitable choice of the evolution and dephasing operators in the neighborhood of the maximal violation line, thereby showing the robustness of temporal correlations under environmental effects.