Witnessing global memory effects of multiqubit correlated noisy channels by Hilbert-Schmidt speed

In correlated noisy channels, the global memory effects on the dynamics of a quantum system depend on both non-Markovianity of the single noisy channel (intrinsic memory) and classical correlations between multiple uses of the channel itself (correlation-based memory). We show that the Hilbert-Schmidt speed (HSS), a measure of non-Markovianity, serves as a reliable figure of merit for evaluating the role of this correlation-based memory on the global memory effects, for both unital and non-unital channels irrespective of initial basis. The intensity of the correlation-based memory is ruled by a classical correlation strength between consecutive applications of the channel. We establish that classical correlation between multiple uses of a channel does not alter the duration of revivals in unital channels, whereas in non-unital channels, it does. Therefore, HSS can serve as an effective tool for distinguishing between unital and non-unital correlated channels. We demonstrate that, for unital noisy channels, increasing the number of qubits of the system significantly weakens the sensitivity of the HSS to this classical correlation strength. Such a pattern indicates that the state evolution of large quantum systems may be less prone to be affected by classical correlations between noisy channels. Moreover, assuming that the qubits are affected by independent or classically correlated local non-Markovian unital channels, we observe that, as the number of qubits increases, the collective behavior of the multiqubit system inhibits the non-Markovian features of the overall system dynamics.