Constructive Feedback of Non-Markovianity on Resources in Random Quantum States

Abstract: We explore the impact of non-Markovian channels on the quantum correlations (QCs) of Haar uniformly generated random two-qubit input states with different ranks -- either one of the qubits (single-sided) or both the qubits independently (double-sided) are passed through noisy channels. Under dephasing and depolarizing channels with varying non-Markovian strength, entanglement and quantum discord of the output states collapse and revive with the increase of noise. We find that in case of the depolarizing double-sided channel, both the QCs of random states show a higher number of revivals on average than that of the single-sided ones with a fixed non-Markovianity strength, irrespective of the rank of the states -- we call such a counter-intuitive event as a constructive feedback of non-Markovianity. Consequently, the average noise at which QCs of random states show first revival decreases with the increase of the strength of non-Markovian noise, thereby indicating the role of non-Markovian channels on the regenerations of QCs even in presence of a high amount of noise. However, we observe that non-Markovianity does not play any role to increase the robustness in random quantum states which can be measured by the mean value of critical noise at which quantum correlations first collapse. Moreover, we observe that the tendency of a state to show regeneration increases with the increase of average QCs of the random input states along with non-Markovianity.