Dynamics of Geometric Measure of Quantum Discord of Two Qubits in Independent Reservoirs

We study the dynamics of geometric measure of quantum discord. The model under consideration is a physical system of two qubits coupled with two independent bosonic reservoirs described by Ohmic-like spectral densities. We aim to find how the system's geometric measure of quantum discord evolves, and whether and in what conditions it may remain constant for a time interval or be frozen forever. Our result shows that by properly choosing the system's initial states, geometric measure of quantum discord may hold a frozen phenomenon in a time interval for all the three types of reservoirs, sub-Ohmic, Ohmic, and super-Ohmic reservoirs, and it may also hold a time-invariant phenomenon for super-Ohmic reservoirs. The conditions satisfied by the coefficients of standard Bell-diagonal states, in which the frozen phenomenon in a time interval or the time-invariant phenomenon of geometric measure of quantum discord appears, are given.