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arXiv:1607.05778 · Physical Review A

PT -symmetric slowing down of decoherence

Bartłomiej Gardas, Sebastian Deffner, Avadh Saxena

Published Oct 27, 2016• 52 citations
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Abstract

We investigate $\mathcal{P}\mathcal{T}$-symmetric quantum systems ultraweakly coupled to an environment. We find that such open systems evolve under $\mathcal{P}\mathcal{T}$-symmetric, purely dephasing and unital dynamics. The dynamical map describing the evolution is then determined explicitly using a quantum canonical transformation. Furthermore, we provide an explanation of why $\mathcal{P}\mathcal{T}$-symmetric dephasing-type interactions lead to a critical slowing down of decoherence. This effect is further exemplified with an experimentally relevant system, a $\mathcal{P}\mathcal{T}$-symmetric qubit easily realizable, e.g., in optical or microcavity experiments.

DOI
10.1103/physreva.94.040101

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We investigate PT\mathcal{P}\mathcal{T}PT-symmetric quantum systems ultraweakly coupled to an environment. We find that such open systems evolve under PT\mathcal{P}\mathcal{T}PT-symmetric, purely dephasing and unital dynamics. The dynamical map describing the evolution is then determined explicitly using a quantum canonical transformation. Furthermore, we provide an explanation of why PT\mathcal{P}\mathcal{T}PT-symmetric dephasing-type interactions lead to a critical slowing down of decoherence. This effect is further exemplified with an experimentally relevant system, a PT\mathcal{P}\mathcal{T}PT-symmetric qubit easily realizable, e.g., in optical or microcavity experiments.
In the past years, many efforts have been made to study various noteworthy phenomena in both parity-time (PT)(\mathcal{PT})(PT) and anti-parity-time (APT)(\mathcal{APT})(APT) symmetric systems. However, entanglement dynamics in APT\mathcal{APT}APT-symmetric systems has not previously been investigated in both theory and experiments. Here, we investigate the entanglement evolution of two qubits in an APT\mathcal{APT}APT-symmetric system. In the APT\mathcal{APT}APT-symmetric unbroken regime, our theoretical simulations demonstrate the periodic oscillations of entanglement when each qubit evolves identically, while the nonperiodic oscillations of entanglement when each qubit evolves differently. In particular, when each qubit evolves near the exceptional point in the APT\mathcal{APT}APT-symmetric unbroken regime, there exist entanglement sudden vanishing and revival. Moreover, our simulations demonstrate rapid decay and delayed death of entanglement provided one qubit evolves in the APT\mathcal{APT}APT-symmetric broken regime. In this work, we also perform an experiment with a linear optical setup. The experimental results agree well with our theoretical simulation results. Our findings reveal novel phenomena of entanglement evolution in the APT\mathcal{APT}APT-symmetric system and opens a new direction for future studies on the dynamics of quantum entanglement in multiqubit APT\mathcal{APT}APT-symmetric systems or other non-Hermitian quantum 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.
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.
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 outline two general classes of examples of PT\mathbb{P}\mathbb{T}PT-symmetric quantum Liouvillian dynamics of open many-qubit systems, namely, interacting hard-core bosons (or more general XYZXYZXYZ-type spin-1/2 systems) having either (i) pure dephasing noise or (ii) solely single-particle (spin) injection (absorption) incoherent processes. The concept of PT\mathbb{P}\mathbb{T}PT symmetry is defined following Prosen [Phys. Rev. Lett. 109, 090404 (2012)] as a formal quantum Liouville-space analog of the parity-time PT\mathcal{PT}PT symmetry used in nonconservative classical systems with symmetrically distributed gain and loss.
Quantum dynamics of two XXXXXX interacting PT-symmetric non-Hermitian qubits: enhancement of quantum annealing
Quantum information platforms enable analog quantum simulations, such as quantum annealing, offering a promising route to solving complex combinatorial optimization problems. Here, we propose a quantum information architecture based on networks of interacting parity-time (PT)-symmetric non-Hermitian qubits. While the dynamics of individual PT-symmetric qubits have been experimentally demonstrated across multiple platforms including NV centers, superconducting circuits, and trapped-ion systems yet coherent dynamics in interacting systems remain largely unexplored. To address this issue we theoretically investigate stationary and time-dependent Hamiltonians relevant to quantum annealing using a minimal model of two interacting XX-coupled PT-symmetric non-Hermitian qubits. We analyze both symmetry-preserving and symmetry-broken regimes and demonstrate that adding even tiny PT-symmetric non-Hermitian terms in the qubits Hamiltonian allows to greatly enhance the probability of reaching the ground state after annealing.