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arXiv:2508.03169

Quantum Dynamics and Information Measures in PT and Anti-PT-Symmetric Systems

Ahmadi, Amir, Asgari, Roozbeh H., Javad T. Firouzjaee

Published Aug 5, 2025• 0 citations
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Abstract

In this study, we investigate qubit dynamics under PT and Anti-PT-symmetric non-Hermitian Hamiltonians, focusing on phase evolution, decoherence, quantum speed limits (QSL), and Rényi entanglement entropies. Using similarity transformations and Dyson maps, we analyze the reduced density matrix evolution in bosonic environments. Anti-PT-symmetric systems show enhanced robustness against decoherence, with slower entropy growth and longer coherence times compared to PT-symmetric counterparts. QSL behavior is non-monotonic, reflecting rapid initial evolution followed by a gradual decrease. Higher-order Rényi entropies reveal that Anti-PT-symmetric qubits preserve quantum information more effectively, offering advantages for memory and cryptographic applications.

DOI
10.48550/arxiv.2508.03169

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In this study, we investigate qubit dynamics under PT and Anti-PT-symmetric non-Hermitian Hamiltonians, focusing on phase evolution, decoherence, quantum speed limits (QSL), and Rényi entanglement entropies. Using similarity transformations and Dyson maps, we analyze the reduced density matrix evolution in bosonic environments. Anti-PT-symmetric systems show enhanced robustness against decoherence, with slower entropy growth and longer coherence times compared to PT-symmetric counterparts. QSL behavior is non-monotonic, reflecting rapid initial evolution followed by a gradual decrease. Higher-order Rényi entropies reveal that Anti-PT-symmetric qubits preserve quantum information more effectively, offering advantages for memory and cryptographic applications.
We investigate the dynamics of a general two-level based anti-parity-time (anti-PT\mathcal{PT}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\mathcal{PT}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\mathcal{PT}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\mathcal{PT}PT-symmetric qubit decays and grows more slowly, respectively, compared to the PT\mathcal{PT}PT-symmetric and Hermitian qubits. Similarly, the corresponding variance and area of Fisher information are much higher compared to the PT\mathcal{PT}PT-symmetric and Hermitian qubits. These results demonstrate that anti-PT\mathcal{PT}PT-symmetric qubits may be better suited for quantum computing and quantum information processing applications than conventional Hermitian or even PT\mathcal{PT}PT-symmetric qubits.
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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 reveal the continuous phase transition in anyonic-PT symmetric systems, contrasting with the discontinuous phase transition corresponding to the discrete (anti-) PT symmetry. The continuous phase transition originates from the continuity of anyonic-PT symmetry. We find there are three information-dynamics patterns for anyonic-PT symmetric systems: damped oscillations with an overall decrease (increase) and asymptotically stable damped oscillations, which are three-fold degenerate and distorted using the Hermitian quantum Rényi entropy or distinguishability. It is the normalization of the non-unitary evolved density matrix causes the degeneracy and distortion. We give a justification for non-Hermitian quantum Rényi entropy being negative. By exploring the mathematics and physical meaning of the negative entropy in open quantum systems, we connect the negative non-Hermitian quantum Rényi entropy and negative quantum conditional entropy, opening up a new journey to rigorously investigate the negative entropy in open quantum systems.
We reveal the continuous change of information dynamics patterns in anyonic-PT symmetric systems that originates from the continuity of anyonic-PT symmetry. We find there are three information dynamics patterns for anyonic-PT symmetric systems: damped oscillations with an overall decrease (increase) and asymptotically stable damped oscillations, which are three-fold degenerate and are distorted using the Hermitian quantum Rényi entropy or distinguishability. It is the normalization of the non-unitary evolved density matrix that causes the degeneracy and distortion. We give a justification for non-Hermitian quantum Rényi entropy being negative. By exploring the mathematics and physical meaning of the negative entropy in open quantum systems, we connect negative non-Hermitian quantum Rényi entropy and negative quantum conditional entropy, paving the way to rigorously investigate negative entropy in open quantum systems.
We have introduced PT-symmetry to a central spin model by adding a PT-symmetric interaction with a tunable hermiticity parameter γγγ. Using the pseudo-Hermitian formalism, we applied a Dyson map to transform the non-Hermitian Hamiltonian to its Hermitian representation. We have found that the decoherence slows down as γγγ increases, eventually ceasing at γ=1γ=1γ=1. We define a pseudo-Hermitian observable that commutes with the metric operator to add as the self-Hamiltonian. Einselection gradually forced the system to select the eigenstates of the self-Hamiltonian as γ→1γ\rightarrow1γ→1. The steady-state purity of the central spin states in the strong environment regime exhibits a paradoxical decrease as γγγ increases. However, a turning point (minimum) corresponding to a maximum information dissipation to the spin bath is found. Finally, the Breuer-Laine-Piilo (BLP) measure, which is used to quantify the non-Markovianity of a quantum system, was evaluated for a finite time. The BLP measure in the strong environment regime exhibited similar turning point behavior, which means that the information backflow reaches a saturation point before declining. This decline signifies the point where PT-symmetry starts shielding the central spin from the environment.