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arXiv:1906.05073 · npj Quantum Information

Observation of information flow in the anti-𝒫𝒯-symmetric system with nuclear spins

Jingwei Wen, Guo‐Qing Qin, Chao Zheng, Shijie Wei, Xiangyu Kong, Tao Xin, Gui‐Lu Long

Published Mar 23, 2020• 48 citations
arXivHTMLPDF

Abstract

Abstract The recently theoretical and experimental researches on $${\mathcal{PT}}$$ PT -symmetric system have attracted unprecedented attention because of the various interesting features and potential applications in extending canonical quantum mechanics. However, as the counterpart of $${\mathcal{PT}}$$ PT -symmetry, there are few experimental researches on the anti- $${\mathcal{PT}}$$ PT -symmetric quantum system because of the challenges in simulating anti- $${\mathcal{PT}}$$ PT -symmetry in experiment. Here, we propose an algorithm for simulating the generalized anti- $${\mathcal{PT}}$$ PT -symmetric system in the quantum circuit model. Utilizing the algorithm, we demonstrated the quantum simulation of anti- $${\mathcal{PT}}$$ PT system experimentally, and an oscillation of information flow is observed in a nuclear magnetic resonance quantum simulator. The experiment showed that the information could recover from the environment completely when the anti- $${\mathcal{PT}}$$ PT -symmetry is broken, whereas no information can be retrieved in the symmetry-unbroken phase. Our work opens the gate for the practical quantum simulation and experimental investigation of universal anti- $${\mathcal{PT}}$$ PT -symmetric system in a quantum computer.

DOI
10.1038/s41534-020-0258-4

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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.
Non-Hermitian systems satisfying parity-time (PT) symmetry have aroused considerable interest owing to their exotic features. Anti-PT symmetry is an important counterpart of the PT symmetry, and has been studied in various classical systems. Although a Hamiltonian with anti-PT symmetry only differs from its PT-symmetric counterpart in a global ±i phase, the information and energy exchange between systems and environment are different under them. It is also suggested theoretically that anti-PT symmetry is a useful concept in the context of quantum information storage with qubits coupled to a bosonic bath. So far, the observation of anti-PT symmetry in individual quantum systems remains elusive. Here, we implement an anti-PT-symmetric Hamiltonian of a single qubit in a single trapped ion by a designed microwave and optical control-pulse sequence. We characterize the anti-PTphase transition by mapping out the eigenvalues at different ratios between coupling strengths and dissipation rates. The full information of the quantum state is also obtained by quantum state tomography. Our work allows quantum simulation of genuine open-system feature of an anti-PT-symmetric system, which paves the way for utilizing non-Hermitian properties for quantum information processing.
We experimentally simulate nonunitary quantum dynamics using a single-photon interferometric network and study the information flow between a parity-time- (PT-)symmetric non-Hermitian system and its environment. We observe oscillations of quantum-state distinguishability and complete information retrieval in the PT-symmetry-unbroken regime. We then characterize in detail critical phenomena of the information flow near the exceptional point separating the PT-unbroken and PT-broken regimes, and demonstrate power-law behavior in key quantities such as the distinguishability and the recurrence time. We also reveal how the critical phenomena are affected by symmetry and initial conditions. Finally, introducing an ancilla as an environment and probing quantum entanglement between the system and the environment, we confirm that the observed information retrieval is induced by a finite-dimensional entanglement partner in the environment. Our work constitutes the first experimental characterization of critical phenomena in PT-symmetric nonunitary quantum dynamics.
Comprehensive study on parity-time (PT) symmetric systems demonstrates the novel properties and innovative application of non-Hermitian physics in recent years. In the quantum regime, PT symmetric physics exhibits unique quantum dynamical behaviors such as spontaneous state-distinguishability oscillation. However, the construction and control of a PT symmetric quantum system are still challenging, that and restrict the experimental investigation of PT symmetric quantum nature and application. In this Letter, we propose and construct a recycling-structure PT symmetric quantum simulator for the first time, which can effectively simulate the discrete-time dynamical process of a PT symmetric quantum system in both unbroken and broken phases, to be different from our previous work [J.-S. Tang, et al., Nat. Photonics 10, 642 (2016)]. We investigate the dynamical features of quantum state distinguishability based on the PT symmetric simulator. Our results demonstrate the novel PT symmetric quantum dynamics characterized by the periodical oscillation of state distinguishability in the unbroken phase, and the monotonic decay of that in the broken phase. This work also provides a practical experimental platform for the future intensive study of PT symmetric quantum dynamics.
The PT -symmetric non-Hermitian systems have been widely studied and explored both in theory and in experiment due to their various interesting features.In this work we focus on the dynamical features of a triplequbit system, one of which evolves under a local PT -symmetric Hamiltonian.An abnormal dynamic pattern in the entropy evolution process is identified that presents a parameter-dependent stable state, determined by the non-Hermiticity of Hamiltonian in the broken phase of PT symmetry.The entanglement and mutual information of a two-body subsystem can increase beyond the initial values, which do not exist in the Hermitian and two-qubit PT -symmetric systems.Moreover, an experimental demonstration of the stable states in non-Hermitian systems with nonzero entropy and entanglement is realized on a four-qubit quantum simulator with nuclear spins.Our work reveals the distinctive dynamic features in the triple-qubit PT -symmetric system and paves the way for practical quantum simulation of multiparty non-Hermitian system on quantum computers.