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arXiv:2207.12624 · Physical Review Research

Distinguishability transitions in nonunitary boson-sampling dynamics

Ken Mochizuki, Ryusuke Hamazaki

Published Mar 14, 2023• 3 citations
arXivHTMLPDF

Abstract

We discover transitions characterized by distinguishability of bosons in nonunitary dynamics with parity-time $(\mathcal{PT})$ symmetry. We show that $\mathcal{PT}$-symmetry breaking, a unique transition in non-Hermitian open systems, enhances regions in which bosons can be regarded as distinguishable. This means that classical computers can sample the boson distributions efficiently in these regions by sampling the distribution of distinguishable particles. In a $\mathcal{PT}$-symmetric phase, we find one dynamical transition upon which the distribution of bosons deviates from that of distinguishable particles, when bosons are initially put at distant sites. If the system enters a $\mathcal{PT}$-broken phase, the threshold time for the transition is suddenly prolonged, since dynamics of each boson is diffusive (ballistic) in the $\mathcal{PT}$-broken ($\mathcal{PT}$-symmetric) phase. Furthermore, the $\mathcal{PT}$-broken phase also exhibits a notable dynamical transition on a longer time scale, at which the bosons again become distinguishable. This transition, and hence the classical easiness of sampling bosons in long times, is true for generic postselected nonunitary quantum dynamics, while it is absent in unitary dynamics of isolated quantum systems. $\mathcal{PT}$-symmetry breaking can also be characterized by the efficiency of a classical algorithm based on the rank of matrices, which can (cannot) efficiently compute the photon distribution in the long-time regime of the $\mathcal{PT}$-broken ($\mathcal{PT}$-symmetric) phase.

DOI
10.1103/physrevresearch.5.013177

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We discover transitions characterized by distinguishability of bosons in nonunitary dynamics with parity-time (PT)(\mathcal{PT})(PT) symmetry. We show that PT\mathcal{PT}PT-symmetry breaking, a unique transition in non-Hermitian open systems, enhances regions in which bosons can be regarded as distinguishable. This means that classical computers can sample the boson distributions efficiently in these regions by sampling the distribution of distinguishable particles. In a PT\mathcal{PT}PT-symmetric phase, we find one dynamical transition upon which the distribution of bosons deviates from that of distinguishable particles, when bosons are initially put at distant sites. If the system enters a PT\mathcal{PT}PT-broken phase, the threshold time for the transition is suddenly prolonged, since dynamics of each boson is diffusive (ballistic) in the PT\mathcal{PT}PT-broken (PT\mathcal{PT}PT-symmetric) phase. Furthermore, the PT\mathcal{PT}PT-broken phase also exhibits a notable dynamical transition on a longer time scale, at which the bosons again become distinguishable. This transition, and hence the classical easiness of sampling bosons in long times, is true for generic postselected nonunitary quantum dynamics, while it is absent in unitary dynamics of isolated quantum systems. PT\mathcal{PT}PT-symmetry breaking can also be characterized by the efficiency of a classical algorithm based on the rank of matrices, which can (cannot) efficiently compute the photon distribution in the long-time regime of the PT\mathcal{PT}PT-broken (PT\mathcal{PT}PT-symmetric) phase.
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.
Recently, impressive progress has been made in the study of non-Hermitian systems with parity-time symmetry, such as observations of topological properties of physical systems and criticality at exceptional points. A crucial aspect of parity-time symmetric nonunitary dynamics is the information flow between the system and the environment. In this paper, we use the physical quantity, distinguishability between quantum states, to uniformly quantify the information flow between low-dimensional and high-dimensional parity-time symmetric non-Hermitian systems and environments. The numerical results show that the oscillation of quantum state distinguishability and complete information retrieval and can be obtained in the parity-time-unbroken phase. However, the information decays exponentially in the parity-time-broken phase. The exceptional point marks the criticality between reversibility and irreversibility of information flow, and the distinguishability between quantum states exhibits the behavior of power-law decay. Understanding these unique phenomena in nonunitary quantum dynamics provides an important perspective for the study of open quantum systems and contributes to their application in quantum information.
Recently, impressive progress has been made in the study of non-Hermitian systems with parity-time symmetry, such as observations of topological properties of physical systems and criticality at exceptional points. A crucial aspect of parity-time symmetric nonunitary dynamics is the information flow between the system and the environment. In this paper, we use the physical quantity, distinguishability between quantum states, to uniformly quantify the information flow between low-dimensional and high-dimensional parity-time symmetric non-Hermitian systems and environments. The numerical results show that the oscillation of quantum state distinguishability and complete information retrieval and can be obtained in the parity-time-unbroken phase. However, the information decays exponentially in the paritytime-broken phase. The exceptional point marks the criticality between reversibility and irreversibility of information flow, and the distinguishability between quantum states exhibits the behavior of power-law decay. Understanding these unique phenomena in nonunitary quantum dynamics provides an important perspective for the study of open quantum systems and contributes to their application in quantum information.
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.
We simulate the dissipative dynamics of a mesoscopic system of long-range interacting particles which can be mapped into non-Hermitian spin models with a PT\mathcal{PT}PT symmetry. We find rich PT\mathcal{PT}PT phase diagrams with PT\mathcal{PT}PT-symmetric and PT\mathcal{PT}PT-broken phases. The dynamical regimes can be further enriched by modulating tunable parameters of the system. We outline how the PT\mathcal{PT}PT symmetries of such systems may be probed by studying their dynamics. We note that systems of Rydberg atoms and systems of Rydberg ions with strong dipolar interactions are particularly well suited for such studies. We present a viable proposal for implementing non-Hermitian physics with PT\mathcal{PT}PT symmetry in Rydberg systems. We show that for realistic parameters, long-range interactions allow the emergence of new PT\mathcal{PT}PT-symmetric regions, generating new PT\mathcal{PT}PT phase transitions. In addition, such PT\mathcal{PT}PT-symmetry phase transitions are found by changing the configurations of the Rydberg atoms. We propose a postselection scheme on an ensemble of Rydberg ions described by an effective three-level system. Detecting the population dynamics, the system shows an oscillatory behavior in the PT\mathcal{PT}PT-unbroken phase and a stationary population for long times in the PT\mathcal{PT}PT-broken phase.
We explore the free boson unitary dynamics subject to repeated random forced measurement. The input state is chosen as a Fock state in real space with the particle number conserved in the entire dynamics. We show that each boson is performing a non-unitary quantum walk in real space and its dynamics can be mapped to directed polymers in a random medium with complex amplitude. We numerically show that in the one dimensional system, when the measurement strength is finite, the system is in the frozen phase with all the bosons localized in the real space. Furthermore, these single particle wave functions take the same probability distribution in real space after long time evolution. Due to this property, the boson sampling for the output state becomes easy to solve. We further investigate circuit with non-local unitary dynamics and numerically demonstrate that there could exist a phase transition from a localized phase to a delocalized phase by varying the measurement strength.