Geometric measure of quantum discord under decoherence

TL;DR

This paper investigates the behavior of a geometric measure of quantum discord under decoherence, providing analytical results for different channels and comparing its dynamics with quantum discord and entanglement.

Contribution

It introduces an alternative method to compute GMQD using singular values and analyzes its dynamics under various decoherence channels.

Findings

GMQD can be obtained from singular values of a specific matrix

Sudden changes in GMQD decay do not always match quantum discord decay

For Bell diagonal states, GMQD and quantum discord change simultaneously

Abstract

The dynamics of a geometric measure of the quantum discord (GMQD) under decoherence is investigated. We show that the GMQD of a two-qubit state can be alternatively obtained through the singular values of a $3\times4$ matrix whose elements are the expectation values of Pauli matrices of the two qubits. By using Heisenberg picture, the analytic results of the GMQD is obtained for three typical kinds of the quantum decoherence channels. We compare the dynamics of the GMQD with that of the quantum discord and of entanglement. We show that a sudden change in the decay rate of the GMQD does not always imply that of the quantum discord, and vice versa. We also give a general analysis on the sudden change in behavior and find that at least for the Bell diagonal states, the sudden changes in decay rates of the GMQD and that of the quantum discord occur simultaneously.