Assessing the quantumness of a damped two-level system

TL;DR

This paper analyzes the nonclassical properties of a damped two-level quantum system, comparing three quantumness criteria and showing their decay over time due to thermal reservoir coupling, linked to the system's coherence half-life.

Contribution

It provides a detailed comparison of three quantumness measures and establishes their decay dynamics and relation to coherence in a damped two-level system.

Findings

All three quantum indicators decay exponentially over time.

The decay times are identical and equal to the coherence half-life.

Violations of Leggett-Garg inequalities are connected to the system's coherence.

Abstract

We perform a detailed analysis of the nonclassical properties of a damped two-level system. We compute and compare three different criteria of quantumness, the $l_1$-norm of coherence, the Leggett- Garg inequality and a quantum witness based on the no-signaling in time condition. We show that all three quantum indicators decay exponentially in time as a result of the coupling to the thermal reservoir. We further demonstrate that the corresponding characteristic times are identical and given by the coherence half-life. These results quantify how violations of Leggett-Garg inequalities and nonzero values of the quantum witness are connected to the coherence of the two-level system.