Dynamical non-Hermitian systems: Fingerprints and pure-dephasing-induced protection effect

Non-Hermitian systems have shown promising potential for realizing quantum information tasks that lack counterparts in the Hermitian realm. Understanding the dynamical characteristics of non-Hermitian systems as reflected in information-theoretic quantities is essential for advancing their applications. Here we investigate dynamics of trace distance and concurrence, which quantify information flow and entanglement, respectively, in non-Hermitian qubit systems exhibiting either parity-time or anti-parity-time symmetry. We identify dynamical fingerprints from the system density matrix which provide a unified explanation to the common oscillation and relaxation dynamics shared by trace distance and concurrence observed in existing studies. We further investigate the fate of dynamical fingerprints under the impact of pure dephasing. Surprisingly, we find that pure dephasing can slow down the inherent relaxation of information flow and entanglement in non-Hermitian systems with unbroken anti-parity-time symmetry, suggesting a passive environment-assisted information protection in this class of non-Hermitian systems. Our findings enhance our understanding of dynamical non-Hermitian systems and have specific relevance to their information-oriented applications.