Conditions for the Freezing Phenomena of Geometric Measure of Quantum Discord for Arbitrary Two-Qubit X-states under Non-dissipative Dephasing Noises

We study the dynamics of geometric measure of quantum discord (GMQD) under the influences of two local phase damping noises. Consider the two qubits initially in arbitrary X-states, we find the necessary and sufficient conditions for which GMQD is unaffected for a finite period. It is further shown that such results also hold for the non-Markovian dephasing process.
Comment: 4 pages, 2 figures