Constructive feedback of non-Markovianity on resources in random quantum states

We explore the impact of non-Markovian channels on the quantum correlations of Haar uniformly generated random two-qubit input states with different ranks: Either one of the qubits (single-sided channel) or both qubits independently (double-sided channel) are passed through a noisy channel. For 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. By both analytical and numerical means, we find that in the case of the depolarizing double-sided channel, entanglement and quantum discord for random states show a higher number of revivals on average than for single-sided channels with a fixed non-Markovianity strength, irrespective of the rank of the states; we call such a counterintuitive event, constructive feedback of non-Markovianity. In contrast, the mean value of critical noise at which quantum correlations (QCs) first collapse decreases with the increase of non-Markovianity, independently of the rank of the random initial states. However, the average noise at which QCs of random states show the first revival decreases with the increase of the strength of non-Markovian noise, thereby indicating the role of non-Markovian channels in the regeneration of QCs even in the presence of a high amount of noise. 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.