Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories

• URL: http://arxiv.org/abs/2002.11620v2
• Date: Thu, 25 Jun 2020 10:57:35 GMT
• Title: Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories
• Authors: Fabrizio Minganti, Adam Miranowicz, Ravindra W. Chhajlany, Ievgen I. Arkhipov, and Franco Nori
• Abstract summary: We introduce a hybrid-Liouvillian superoperator capable of describing the passage from an NHH (when one postselects only those trajectories without quantum jumps) to a true Liouvillian including quantum jumps (without postselection) Our approach allows to intuitively relate the effects of postselection and finite-efficiency detectors.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Exceptional points (EPs) are degeneracies of classical and quantum open systems, which are studied in many areas of physics including optics, optoelectronics, plasmonics, and condensed matter physics. In the semiclassical regime, open systems can be described by phenomenological effective non-Hermitian Hamiltonians (NHHs) capturing the effects of gain and loss in terms of imaginary fields. The EPs that characterize the spectra of such Hamiltonians (HEPs) describe the time evolution of a system without quantum jumps. It is well known that a full quantum treatment describing more generic dynamics must crucially take into account such quantum jumps. In a recent paper [F. Minganti $et$ $al.$, Phys. Rev. A $\mathbf{100}$, $062131$ ($2019$)], we generalized the notion of EPs to the spectra of Liouvillian superoperators governing open system dynamics described by Lindblad master equations. Intriguingly, we found that in situations where a classical-to-quantum correspondence exists, the two types of dynamics can yield different EPs. In a recent experimental work [M. Naghiloo $et$ $al.$, Nat. Phys. $\mathbf{15}$, $1232$ ($2019$)], it was shown that one can engineer a non-Hermitian Hamiltonian in the quantum limit by postselecting on certain quantum jump trajectories. This raises an interesting question concerning the relation between Hamiltonian and Lindbladian EPs, and quantum trajectories. We discuss these connections by introducing a hybrid-Liouvillian superoperator, capable of describing the passage from an NHH (when one postselects only those trajectories without quantum jumps) to a true Liouvillian including quantum jumps (without postselection). Beyond its fundamental interest, our approach allows to intuitively relate the effects of postselection and finite-efficiency detectors.

Related papers

• Encircling the Liouvillian exceptional points: a brief review [1.5596062401801003]
  Liouvillian exceptional points often have distinct properties compared to their counterparts in non-Hermitian Hamiltonians. Since the Liouvillian exceptional points widely exist in quantum systems such as the atomic vapours, superconducting qubits, and ultracold ions and atoms, they have received increasing amount of attention of late.
  arXiv  Detail & Related papers  (2024-08-21T08:46:04Z)
• Magnetization in a non-equilibrium quantum spin system [0.0]
  We show that the effective non-Hermitian Hamiltonian can accurately represent the long-term dynamics of a critical two-level open quantum system. The NESS is identical to the coalescent state of the effective non-Hermitian Hamiltonian. This discovery paves the way for a better understanding of the long-term dynamics of critical open quantum systems.
  arXiv  Detail & Related papers  (2024-06-01T02:16:24Z)
• Quantum State Transfer in Interacting, Multiple-Excitation Systems [41.94295877935867]
  Quantum state transfer (QST) describes the coherent passage of quantum information from one node to another. We describe Monte Carlo techniques which enable the discovery of a Hamiltonian that gives high-fidelity QST. The resulting Jaynes-Cummings-Hubbard and periodic Anderson models can, in principle, be engineered in appropriate hardware to give efficient QST.
  arXiv  Detail & Related papers  (2024-05-10T23:46:35Z)
• Liouvillian Exceptional Points of Non-Hermitian Systems via Quantum Process Tomography [0.0]
  Hamiltonian exceptional points are spectral degeneracies of non-Hermitian Hamiltonians. quantum process tomography can be readily applied to reveal and characterize LEPs of non-Hermitian systems.
  arXiv  Detail & Related papers  (2024-01-26T16:47:26Z)
• Mixed Quantum-Semiclassical Simulation [0.0]
  We study the quantum simulation of mixed quantum-semiclassical (MQS) systems, of fundamental interest in many areas of physics. A basic question for these systems is whether quantum algorithms of MQS systems would be valuable at all, when one could instead study the full quantum-quantum system.
  arXiv  Detail & Related papers  (2023-08-30T17:02:33Z)
• Observing super-quantum correlations across the exceptional point in a single, two-level trapped ion [48.7576911714538]
  In two-level quantum systems - qubits - unitary dynamics theoretically limit these quantum correlations to $2qrt2$ or 1.5 respectively. Here, using a dissipative, trapped $40$Ca$+$ ion governed by a two-level, non-Hermitian Hamiltonian, we observe correlation values up to 1.703(4) for the Leggett-Garg parameter $K_3$. These excesses occur across the exceptional point of the parity-time symmetric Hamiltonian responsible for the qubit's non-unitary, coherent dynamics.
  arXiv  Detail & Related papers  (2023-04-24T19:44:41Z)
• Guidable Local Hamiltonian Problems with Implications to Heuristic Ansätze State Preparation and the Quantum PCP Conjecture [0.0]
  We study 'Merlinized' versions of the recently defined Guided Local Hamiltonian problem. These problems do not have a guiding state provided as a part of the input, but merely come with the promise that one exists. We show that guidable local Hamiltonian problems for both classes of guiding states are $mathsfQCMA$-complete in the inverse-polynomial precision setting.
  arXiv  Detail & Related papers  (2023-02-22T19:00:00Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Genuine multipartite entanglement and quantum coherence in an electron-positron system: Relativistic covariance [117.44028458220427]
  We analyze the behavior of both genuine multipartite entanglement and quantum coherence under Lorentz boosts. A given combination of these quantum resources is shown to form a Lorentz invariant.
  arXiv  Detail & Related papers  (2021-11-26T17:22:59Z)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)
• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond [46.39654665163597]
  We report on experimental tests of topological defect formation via the one-dimensional transverse-field Ising model. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system.
  arXiv  Detail & Related papers  (2020-01-31T02:55:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.