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

TL;DR

This paper investigates how global memory effects in multiqubit noisy channels are influenced by classical correlations and non-Markovianity, using Hilbert-Schmidt speed as a key measure, revealing that larger systems are less sensitive to classical correlations.

Contribution

It demonstrates that Hilbert-Schmidt speed effectively evaluates correlation-based memory effects and shows that increasing qubits diminishes sensitivity to classical correlations and non-Markovian features.

Findings

Hilbert-Schmidt speed reliably measures non-Markovianity in correlated channels.

Increasing qubits weakens the impact of classical correlations on system dynamics.

Large quantum systems are less affected by classical correlations and non-Markovian effects.

Abstract

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. The intensity of the correlation-based memory is ruled by a classical correlation strength between consecutive applications of the channel. 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 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.