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.
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.
Understanding the dynamical evolution of non-Hermitian systems under external dissipation is essential for devising realistic non-Hermitian quantum devices that surpass the capabilities of their Hermitian counterparts. Dephasing, a major realistic dissipation, has an impact on non-Hermitian systems that remains largely unexplored. Here, we focus on finite-sized non-Hermitian Su-Schrieffer-Heeger (SSH) lattice models with alternating gain and loss in real space and examine the dynamical evolution of the trace distance under pure dephasing. By tuning system parameters, this model supports phases with either parity-time or anti-parity-time symmetries, enabling us to explore the dephasing effect across different non-Hermitian symmetry regimes within a single platform. While the trace distance exhibits distinct dynamical behaviors across the different phases in the absence of dephasing, its response to dephasing is largely symmetry-independent but instead initial-state dependent. By varying the initial states, we find that dephasing affects the trace distance in two qualitatively different ways. For initial states that differ only in their coherences, dephasing accelerates the decay of the trace distance, destroying the phase information in much the same way as in Hermitian systems. In contrast, for initial states that differ only in their populations, strong dephasing can partially or completely stabilize the trace distance over a wide transient regime before its eventual decay. We attribute these metastable stabilization phenomena to the alternating gain and loss in the system and confirm their absence in Hermitian counterparts. Our findings reveal the intricate dynamical response of non-Hermitian SSH models to dephasing, thereby facilitating their potential applications.
Abstract The evolution of entanglement in a non-Hermitian quantum system may behave differently compared to its Hermitian counterpart. In this paper, we investigate the entanglement dynamics of two coupled and driven non-Hermitian qubits. Through calculating the concurrence of the system, we find that the evolution of the bipartite entanglement manifests two distinct patterns in the parameter space. In the low non-Hermiticity regime, the concurrence oscillates significantly, while in the opposite regime the same quantity would trend to a stable value. We attribute this phenomenon to parity-time ( PT ) symmetry phase transition. We also study the effect of decoherence on the entanglement dynamics. Our work provides a method to stabilize entanglement by exploiting non-Hermiticity.
Theoretical investigation of dynamics and concurrence of entangled PT and anti-PT symmetric polarized photons
Non-Hermitian systems with parity-time [Formula: see text] symmetry and anti-parity-time [Formula: see text] symmetry have exceptional points (EPs) resulting from eigenvector co-coalescence with exceptional properties. In the quantum and classical domains, higher-order EPs for [Formula: see text] symmetry and [Formula: see text]-symmetry systems have been proposed and realized. Both two-qubits [Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text] symmetric systems have seen an increase in recent years, especially in the dynamics of quantum entanglement. However, to our knowledge, neither theoretical nor experimental investigations have been conducted for the dynamics of two-qubits entanglement in the [Formula: see text]-[Formula: see text] symmetric system. We investigate the [Formula: see text]-[Formula: see text] dynamics for the first time. Moreover, we examine the impact of different initial Bell-state conditions on entanglement dynamics in [Formula: see text]-[Formula: see text], [Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text] symmetric systems. Additionally, we conduct a comparative study of entanglement dynamics in the [Formula: see text]-[Formula: see text] symmetrical system, [Formula: see text]-[Formula: see text] symmetrical system, and [Formula: see text]-[Formula: see text] symmetrical systems in order to learn more about non-Hermitian quantum systems and their environments. Entangled qubits evolve in a [Formula: see text]-[Formula: see text] symmetric unbroken regime, the entanglement oscillates with two different oscillation frequencies, and the entanglement is well preserved for a long period of time for the case when non-Hermitian parts of both qubits are taken quite away from the exceptional points.
We investigate the dynamics of a general two-level based anti-parity-time (anti-PT)-symmetric qubit and study its decoherence as well as entanglement entropy properties. We compare our findings with that of the corresponding parity-time (PT)-symmetric and Hermitian qubits. To begin, we consider the time-dependent Dyson map to find the exact analytical dynamics for a general non-Hermitian qubit system weakly coupled with a thermal bath for pure dephasing, before specializing it to the case of a general anti-PT-symmetric qubit. Basing the comparison under the same coupling strength or increasing the non-Hermiticity, we observe that the decoherence function and entanglement entropy of the anti-PT-symmetric qubit decays and grows more slowly, respectively, compared to the PT-symmetric and Hermitian qubits. Similarly, the corresponding variance and area of Fisher information are much higher compared to the PT-symmetric and Hermitian qubits. These results demonstrate that anti-PT-symmetric qubits may be better suited for quantum computing and quantum information processing applications than conventional Hermitian or even PT-symmetric qubits.
We investigate the dephasing dynamics of a qubit as an effective mechanism for estimating the temperature of its surrounding environment for different symmetries. Our approach is fundamentally quantum, leveraging the qubit’s susceptibility to decoherence without necessitating thermal equilibrium with the system under study. We also examine how symmetry properties affect the accuracy of information retrieval and the robustness of quantum information storage in such systems, highlighting their potential advantages in mitigating decoherence effects. The optimization of quantum Fisher information is performed with respect to both the interaction duration and the environmental temperature, focusing on Ohmic-like spectral density environments. Furthermore, we explicitly identify the optimal qubit measurement that attains the quantum Cramér–Rao bound for precision. Our findings reveal that optimal estimation arises from a complex interplay between the qubit’s dephasing dynamics and the Ohmic characteristics of the environment, with a particular focus on non-Hermitian systems that exhibit enhanced resilience to decoherence. We examine the decoherence dynamics of a two-level spin system governed by an anti-parity-time-symmetric Hamiltonian. The obtained results are systematically compared with those corresponding to both PT-symmetric and conventional Hermitian qubit models. To this end, we first employ a time-dependent Dyson transformation to derive the exact analytical evolution of a generic non-Hermitian qubit interacting with an external environment. The formalism is then applied to the particular case of an anti-PT-symmetric qubit. Our analysis reveals that the coherence of the non-Hermitian-symmetric qubit is preserved over significantly longer times, as evidenced by the slower decay of its decoherence function relative to its Hermitian counterparts. Furthermore, the generation of entanglement entropy is found to proceed at a reduced rate, indicating a more gradual buildup of system–environment correlations. In addition, the anti-PT-symmetric configuration exhibits substantially enhanced quantum Fisher information together with a smaller variance than those observed in the corresponding PT-symmetric and Hermitian systems. These findings highlight the remarkable robustness of anti-PT-symmetric qubits against environmental decoherence and suggest that they constitute a promising platform for the implementation of quantum information processing and quantum computing protocols.
We construct new types of two-level qubit systems through incorporating non-Hermiticity with joint Parity-Time and anti-Parity-Time symmetries and present a framework to analytically find the dynamics for such systems. As a result, observe improved properties of decoherence, von Neumann entanglement entropy and quantum Fisher information. This suggests that non-Hermitian PT and APT-symmetric qubits may be better suited for quantum computing and quantum information processing than conventional Hermitian qubits.