Quantum retrodiction in Gaussian systems and applications in optomechanics

• URL: http://arxiv.org/abs/2309.03507v1
• Date: Thu, 7 Sep 2023 06:36:11 GMT
• Title: Quantum retrodiction in Gaussian systems and applications in optomechanics
• Authors: Jonas Lammers, Klemens Hammerer
• Abstract summary: The task of quantum state retrodiction is rigorously and elegantly addressed in quantum measurement theory. This article presents its practical formulation for retrodicting Gaussian quantum states using continuous-time homodyne measurements. We identify and achievable retrodictive POVMs in common optomechanical operating modes with resonant or off-resonant driving fields.
• Score: 0.9065034043031668
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: What knowledge can be obtained from the record of a continuous measurement about the quantum state the measured system was in at the beginning of the measurement? The task of quantum state retrodiction, the inverse of the more common state prediction, is rigorously and elegantly addressed in quantum measurement theory through retrodictive Positive Operator Valued Measures. This article provides an introduction to this general framework, presents its practical formulation for retrodicting Gaussian quantum states using continuous-time homodyne measurements, and applies it to optomechanical systems. We identify and characterise achievable retrodictive POVMs in common optomechanical operating modes with resonant or off-resonant driving fields and specific choices of local oscillator frequencies in homodyne detection. In particular, we demonstrate the possibility of a near-ideal measurement of the quadrature of the mechanical oscillator, giving direct access to the position or momentum distribution of the oscillator at a given time. This forms the basis for complete quantum state tomography, albeit in a destructive manner.

Related papers

• Thermalization and Criticality on an Analog-Digital Quantum Simulator [133.58336306417294]
  We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions. We digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization.
  arXiv  Detail & Related papers  (2024-05-27T17:40:39Z)
• Effect of the readout efficiency of quantum measurement on the system entanglement [44.99833362998488]
  We quantify the entanglement for a particle on a 1d quantum random walk under inefficient monitoring. We find that the system's maximal mean entanglement at the measurement-induced quantum-to-classical crossover is in different ways by the measurement strength and inefficiency.
  arXiv  Detail & Related papers  (2024-02-29T18:10:05Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• Classical Tracking for Quantum Trajectories [1.284647943889634]
  Quantum state estimation, based on the numerical integration of master equations (SMEs), provides estimates for the evolution of quantum systems. We show that classical tracking methods based on particle filters can be used to track quantum states.
  arXiv  Detail & Related papers  (2022-02-01T08:39:19Z)
• Quantum non-demolition measurements of moving target states [0.0]
  We present a protocol for probing the state of a quantum system by its resonant coupling and entanglement with a meter system. We infer the evolution of the entangled systems and, ultimately, the state and dynamics of the system of interest.
  arXiv  Detail & Related papers  (2022-01-11T12:54:41Z)
• Characterizing quantum instruments: from non-demolition measurements to quantum error correction [48.43720700248091]
  In quantum information processing quantum operations are often processed alongside measurements which result in classical data. Non-unitary dynamical processes can take place on the system, for which common quantum channel descriptions fail to describe the time evolution. Quantum measurements are correctly treated by means of so-called quantum instruments capturing both classical outputs and post-measurement quantum states.
  arXiv  Detail & Related papers  (2021-10-13T18:00:13Z)
• From geometry to coherent dissipative dynamics in quantum mechanics [68.8204255655161]
  We work out the case of finite-level systems, for which it is shown by means of the corresponding contact master equation. We describe quantum decays in a 2-level system as coherent and continuous processes.
  arXiv  Detail & Related papers  (2021-07-29T18:27:38Z)
• Efficiently Fuelling a Quantum Engine with Incompatible Measurements [0.0]
  We present two protocols for work extraction, respectively based on single-shot and time-continuous quantum measurements. We relate the extractable work to the noise added by quadrature measurements, and present exact results for the work distribution at arbitrary finite time.
  arXiv  Detail & Related papers  (2021-07-28T09:32:35Z)
• Stochastic Path Integral Analysis of the Continuously Monitored Quantum Harmonic Oscillator [0.0]
  We deduce the evolution equations for position and momentum expectation values and the covariance matrix elements from the system's characteristic function. Our results provide insights into the time dependence of the system during the measurement process, motivating their importance for quantum measurement engine/refrigerator experiments.
  arXiv  Detail & Related papers  (2021-03-10T15:04:49Z)
• Quantum Zeno effect appears in stages [64.41511459132334]
  In the quantum Zeno effect, quantum measurements can block the coherent oscillation of a two level system by freezing its state to one of the measurement eigenstates. We show that the onset of the Zeno regime is marked by a $textitcascade of transitions$ in the system dynamics as the measurement strength is increased.
  arXiv  Detail & Related papers  (2020-03-23T18:17:36Z)
• Coherent states of parametric oscillators in the probability representation of quantum mechanics [0.0]
  The possibility to describe quantum states by tomographic probability distributions (tomograms) is presented. The integrals of motion linear in the position and momentum are used to explicitly obtain the tomogram evolution.
  arXiv  Detail & Related papers  (2020-03-01T12:10:48Z)

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.