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Physical Review A

Anti- PT -symmetric qubit: Decoherence and entanglement entropy

Julia Cen, Avadh Saxena

Published Feb 7, 2022• 14 citations
Publisher

Abstract

We investigate the dynamics of a general two-level based anti-parity-time (anti-$\mathcal{PT}$)-symmetric qubit and study its decoherence as well as entanglement entropy properties. We compare our findings with that of the corresponding parity-time ($\mathcal{PT}$)-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-$\mathcal{PT}$-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-$\mathcal{PT}$-symmetric qubit decays and grows more slowly, respectively, compared to the $\mathcal{PT}$-symmetric and Hermitian qubits. Similarly, the corresponding variance and area of Fisher information are much higher compared to the $\mathcal{PT}$-symmetric and Hermitian qubits. These results demonstrate that anti-$\mathcal{PT}$-symmetric qubits may be better suited for quantum computing and quantum information processing applications than conventional Hermitian or even $\mathcal{PT}$-symmetric qubits.

DOI
10.1103/physreva.105.022404

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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.
Anti-PT\mathcal{PT}PT-symmetric Qubit: Decoherence and Entanglement Entropy
We investigate a two-level spin system 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 PT\mathcal{PT}PT-symmetric and Hermitian qubits. First we consider the time-dependent Dyson map to find the exact analytical dynamics for a general non-Hermitian qubit system coupled with a bath, then we specialize it to the case of the anti-PT\mathcal{PT}PT-symmetric qubit. We find that the decoherence function for the anti-PT\mathcal{PT}PT-symmetric qubit decays slower than the PT\mathcal{PT}PT-symmetric and Hermitian qubits. For the entanglement entropy we find that for the anti-PT\mathcal{PT}PT-symmetric qubit it grows more slowly compared to the PT\mathcal{PT}PT-symmetric and Hermitian qubits. Similarly, we find that the corresponding variance and area of Fisher information is 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.
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.
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 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.
Abstract Non-Hermitian parity-time ( PT{{{{{{{\mathcal{P}}}}}}}}{{{{{{{\mathcal{T}}}}}}}}PT P T ) and anti-parity-time ( APT{{{{{{{\mathcal{APT}}}}}}}}APT APT )-symmetric systems exhibit novel quantum properties and have attracted increasing interest. Although many counterintuitive phenomena in PT{{{{{{{\mathcal{P}}}}}}}}{{{{{{{\mathcal{T}}}}}}}}PT P T - and APT{{{{{{{\mathcal{APT}}}}}}}}APT APT -symmetric systems were previously studied, coherence flow has been rarely investigated. Here, we experimentally demonstrate single-qubit coherence flow in PT{{{{{{{\mathcal{P}}}}}}}}{{{{{{{\mathcal{T}}}}}}}}PT P T - and APT{{{{{{{\mathcal{APT}}}}}}}}APT APT -symmetric systems using an optical setup. In the symmetry unbroken regime, we observe different periodic oscillations of coherence. Particularly, we observe two complete coherence backflows in one period in the PT{{{{{{{\mathcal{P}}}}}}}}{{{{{{{\mathcal{T}}}}}}}}PT P T -symmetric system, while only one backflow in the APT{{{{{{{\mathcal{APT}}}}}}}}APT APT -symmetric system. Moreover, in the symmetry broken regime, we observe the phenomenon of stable value of coherence flow. We derive the analytic proofs of these phenomena and show that most experimental data agree with theoretical results within one standard deviation. This work opens avenues for future study on the dynamics of coherence in PT{{{{{{{\mathcal{P}}}}}}}}{{{{{{{\mathcal{T}}}}}}}}PT P T - and APT{{{{{{{\mathcal{APT}}}}}}}}APT APT -symmetric systems.
We investigate the decoherence in a PT -symmetric qubit coupled with a bosonic bath. Using canonical transformations, we map the non-Hermitian Hamiltonian representing the PT-symmetric qubit to a spin boson model. Identifying the parameter α that demarcates the hermiticity and non-hermiticity in the model, we show that the qubit does not decohere at the transition from the real eigen spectrum to a complex eigen spectrum. Using a general class of spectral densities, the strong suppression of the decoherence is observed due to both vacuum and thermal fluctuations of the bath, and the initial correlations hold, as we approach the transition point.