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arXiv:2607.25561

Interaction-Endowed PT-Symmetry and its Effects on Decoherence, Einselection, and Non-Markovianity in a Central Spin Model

Leoj Phoebe M. Esquierdo, Lemuel John F. Sese, Rayda P. Gammag

quant-phcond-mat.stat-mechSubmitted Jul 28, 2026• Announced Jul 29, 2026• 0 citations
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Abstract

We have introduced PT-symmetry to a central spin model by adding a PT-symmetric interaction with a tunable hermiticity parameter $γ$. 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 $γ$ increases, eventually ceasing at $γ=1$. 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 $γ\rightarrow1$. The steady-state purity of the central spin states in the strong environment regime exhibits a paradoxical decrease as $γ$ 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.

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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.
Abstract Non-Markovian dynamics is central to quantum information processing, as memory effects strongly influence coherence preservation, metrology, and communication. In this work, we investigate the role of stochastic system–bath couplings in shaping non-Markovian behavior of open quantum systems, using the central spin model within a time-convolutionless master equation framework. We show that the character of the reduced dynamics depends jointly on the intrinsic memory of the environment and on the structure of the system–environment interaction. In certain regimes, the dynamics simplify to pure dephasing, while in general both amplitude damping and dephasing contribute to the evolution. By employing two complementary measures: the Quantum Fisher Information (QFI) flow and the Breuer–Laine–Piilo (BLP) measure, we demonstrate that QFI flow may fail to witness memory effects in weak-coupling and near-resonant regimes, whereas the BLP measure still detects information backflow. Furthermore, external modulation of the interaction kernel produces qualitatively richer behavior, including irregular and frequency-dependent revivals of non-Markovianity. These results clarify the physical origin of memory effects, highlight the limitations of single-witness approaches, and suggest that stochasticity and modulation can be harnessed to engineer robust, noise-resilient quantum technologies.
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.
Quantum system tend to have information lost from transmission through the correlations generated among degrees of freedom. For situations where we have a non-Markovian environment, the information contained in it may return to the system, and non-Markovian witnesses can capture such effect. In the present work, we sought how the environment structure affects the system information reachability since its finite size induces a quasiperiodic behavior in the decoherence and enables a highly non-Markovian behavior in the dynamics. To do that, we use a central qubit coupled to a spin chain with Ising interactions subject to a magnetic field, i.e., a central spin model, and solve the exact dynamics of the system. Moreover, we use two witnesses to analyze the presence of non-Markovianity: the Breuer-Laine-Piilo (BLP) trace distance-based measure and the conditional past-future correlator (CPF). On the other hand, we see how such behavior suppresses the classic plateau in Partial Information Plot (PIP) from the paradigm of quantum Darwinism and objective information from Spectrum Broadcast Structure (SBS). In addition to the system point of view, we show that the environmental structure avoids encoding accessible and distinguishable information for measurement in the environment for any model limit. Finally, he orthogonality between the density operators decodes the distinguishability between SBS states in the environment.
In the presence of Lindblad decoherence, i.e., dissipative effects in an open quantum system due to interaction with an environment, we examine the transition probabilities between the eigenstates in the two-level quantum system described by non-Hermitian Hamiltonians with the Lindblad equation, for which the parity-time-reversal (PT) symmetry is conserved. First, the density matrix formalism for PT\mathcal{PT}PT-symmetric non-Hermitian Hamiltonian systems is developed. It is shown that the Lindblad operators Lj{L}_{j}^{}Lj​ are pseudo-Hermitian, namely, $\ensuremath{\eta}{L}_{j}^{}{\ensuremath{\eta}}^{\ensuremath{-}1}={L}_{j}^{\ifmmode\dagger\else\textdagger\fi{}}$ with $\ensuremath{\eta}$ being a linear and positive-definite metric, and respect the PT\mathcal{PT}PT symmetry as well. We demonstrate that the generalized density matrix ${\ensuremath{\rho}}_{\mathrm{G}}^{}(t)\ensuremath{\equiv}\ensuremath{\rho}(t)\ensuremath{\eta}$, instead of the normalized density matrix ${\ensuremath{\rho}}_{\mathrm{N}}^{}(t)\ensuremath{\equiv}\ensuremath{\rho}(t)/\mathrm{tr}\left[\ensuremath{\rho}(t)\right]$, should be implemented for the calculation of the transition probabilities in accordance with the linearity requirement. Second, the density matrix formalism is used to derive the transition probabilities in general cases of PT\mathcal{PT}PT-symmetric non-Hermitian Hamiltonians. In some concrete examples, we calculate compact analytical formulas for the transition probabilities and explore their main features with numerical illustrations. We also make a comparison between our present results and our previous ones using state vectors in the absence of Lindblad decoherence.
Abstract A P T -symmetric, non-Hermitian Hamiltonian in the P T -unbroken regime can lead to unitary dynamics under the appropriate choice of the Hilbert space. The Hilbert space is determined by a Hamiltonian-compatible inner product map on the underlying vector space, facilitated by a ‘metric operator’. A more traditional method, however, involves treating the evolution as open system dynamics, and the state is constructed through normalization at each time step. In this work, we present a comparative study of the two methods of constructing the reduced dynamics of a system evolving under a P T -symmetric Hamiltonian. Our system is a one-dimensional quantum walk with the spin and position degrees of freedom forming its two subsystems. We compare the information flow between the subsystems under the two methods. We find that under the metric formalism, a power law decay of the information backflow to the subsystem gives a clear indication of the transition from P T -unbroken to the broken phase. This is unlike the information backflow under the normalized state method. We also note that even though non-Hermiticity models open system dynamics, pseudo-Hermiticity can increase entanglement between the subsystem in the metric Hilbert space, thus indicating that pseudo-Hermiticity cases can be seen as a resource in quantum mechanics.
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.