Dissipative dynamics of quantum correlation quantifiers under decoherence channels

TL;DR

This paper analyzes how quantum correlations, measured by discord, evolve under decoherence in two-qubit states, providing analytical expressions for preservation and sudden change times, with implications for quantum information in noisy environments.

Contribution

It offers analytical formulas for the dynamics of quantum discord under decoherence, revealing phenomena like preservation, sudden change, and revival, and explores their hierarchy and robustness.

Findings

Derived analytical expressions for decoherence probabilities at sudden change points.

Identified the inverse relationship between the duration of trace distance discord changes and channel operation count.

Established constraint relations for decoherence probabilities under local independent channels.

Abstract

In this work, we investigate the dynamics of quantum correlations captured by entropic and geometric measures of discord under the influence of dissipative channels for widely used two qubit X state with maximally mixed marginals. Identifying the phenomena of the preservation, sudden change and revival of quantum correlation quantifiers, we determine their hierarchy of robustness under memory-less decoherence channels. We find the analytical expressions of decoherence probabilities at which sudden change occur when the first qubit is subjected to the decoherence channels for multiple times. We deduce the exact analytical expression for the preservation time, the duration for which quantum correlations remain unaffected by noise. We also find the time duration between the two sudden change phenomena of trace distance discord, and show its inverse proportionality to the number of times a channel operates on the state. The constraint relations of decoherence probabilities corresponding to the sudden change region and preservation phenomena are obtained when both the qubits are subjected to locally independent quantum channels for multiple times. Our investigation provides physical insights and possible practical implementation of the discord measures in noisy environments.