Parameter Estimation in a Continuously Monitored Non-Markovian Quantum System

• URL: http://arxiv.org/abs/2607.15978v1
• Date: Fri, 17 Jul 2026 14:10:54 GMT
• Title: Parameter Estimation in a Continuously Monitored Non-Markovian Quantum System
• Abstract summary: Continuous monitoring is a powerful tool for analyzing quantum systems.<n>We propose a method based on the reaction coordinate mapping to extend these parameter-estimation techniques beyond the Markovian regime.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Continuous monitoring is a powerful tool for analyzing quantum systems and is increasingly used as a non-demolition technique in quantum metrology. In this context, noisy data acquired through continuous monitoring can be used to precisely pinpoint unknown parameters of the system. However, extending the theoretical framework that connects these data to the underlying parameters beyond Markovian dynamics is notoriously difficult, primarily because such dynamics cannot be expressed as completely positive divisible maps. To overcome this, we propose a method based on the reaction coordinate mapping to extend these parameter-estimation techniques beyond the Markovian regime. Our approach specifically targets linear systems with non-Markovian dynamics undergoing Gaussian continuous measurements, such as homodyne detection. Within this framework, we analyze Bayesian estimation and provide an analytical expression for the Fisher information, alongside the asymptotic scaling of the estimation precision for arbitrary parameters. Finally, we demonstrate the efficacy of our method through the example of thermometry of a bosonic bath.

Related papers

• A machine learning framework for uncovering stochastic nonlinear dynamics from noisy data [35.634572760830764]
  Noise influences the inference of system parameters and ignore dynamics from data.<n>We develop a hybrid symbolic regression-probabilistic machine learning framework that recovers the symbolic form of the governing equations while simultaneously inferring uncertainty in the system parameters.<n>The framework is data-efficient, requiring as few as 100-1000 data points, and robust to noise - demonstrating its broad potential in domains where uncertainty is intrinsic and both the structure and variability of dynamical systems must be understood.
  arXiv  Detail & Related papers  (2026-04-07T16:59:40Z)
• pDANSE: Particle-based Data-driven Nonlinear State Estimation from Nonlinear Measurements [55.95348868409957]
  We consider the problem of designing a data-driven nonlinear state estimation (DANSE) method that uses (noisy) nonlinear measurements.<n>A recurrent neural network (RNN) provides parameters of a Gaussian prior that characterize the state of the model-free process.<n>The second-order statistics of the state posterior are computed using the nonlinear measurements observed at the time point.
  arXiv  Detail & Related papers  (2025-10-31T14:26:48Z)
• Computable measures of non-Markovianity for Gaussian free fermion systems [0.0]
  We investigate measures of non-Markovianity in open quantum systems governed by free fermionic dynamics.<n>For Gaussian states, trace-based distances -- specifically the Hilbert-Schmidt norm -- and second-order R'enyi mutual information can be efficiently expressed.
  arXiv  Detail & Related papers  (2025-09-30T08:47:20Z)
• Reconstructing Quantum States and Expectations via Dynamical Tomography [0.0]
  In quantum systems, an informationally-complete set of observables is not needed for state reconstruction via tomographic techniques.<n>This idea leads to dynamical quantum tomography, whose feasibility we characterize for general quantum dynamics.<n>The framework is illustrated with applications to a spin chain (with or without dissipation) and an electron-nuclear system.
  arXiv  Detail & Related papers  (2025-09-29T11:43:52Z)
• Measurement-induced phase transition in interacting bosons from most likely quantum trajectory [44.61740865424298]
  We show how such trajectory can be identified from the probability distribution of quantum trajectories.<n>We prove the method to be exact in the case of Gaussian theories and then extend it to the interacting Sine-Gordon model.<n>Although no longer exact in this framework, the method captures the dynamics through a self-consistent time-dependent harmonic approximation.
  arXiv  Detail & Related papers  (2025-09-29T09:37:01Z)
• Current-based metrology with two-terminal mesoscopic conductors [11.663587862869102]
  In open quantum systems, an alternative approach to metrology involves the measurement of currents flowing from the system to its environment.<n>We identify the key elements that determine estimation precision within the Landauer-B"uttiker formalism.<n>We obtain analytical results for the precision in linear-response regimes and zero-temperature regimes.
  arXiv  Detail & Related papers  (2025-07-17T08:50:37Z)
• Double Debiased Machine Learning for Mediation Analysis with Continuous Treatments [38.70412001488559]
  We propose a machine learning algorithm for mediation analysis that supports continuous treatments.<n>We provide a numerical evaluation of our approach on a simulation along with an application to real-world medical data to analyze the effect of glycemic control on cognitive functions.
  arXiv  Detail & Related papers  (2025-03-08T10:46:47Z)
• Parameters estimation by fitting correlation functions of continuous quantum measurement [0.0]
  We propose a simple method to estimate the parameters of a continuously measured quantum system, by fitting correlation functions of the measured signal. We demonstrate the approach in simulation, both on toy examples and on a recent superconducting circuits.
  arXiv  Detail & Related papers  (2024-10-15T18:00:08Z)
• Combining critical and quantum metrology [0.0]
  We introduce an approach combining two methodologies into a unified protocol applicable to closed and driven-dissipative systems. We provide analytical expressions for the quantum and classical Fisher information in such a setup, elucidating as well a straightforward measurement approach. We showcase these results by focusing on the squeezing Hamiltonian, which characterizes the thermodynamic limit of Dicke and Lipkin-Meshkov-Glick Hamiltonians.
  arXiv  Detail & Related papers  (2023-11-28T04:21:39Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• Leveraging Global Parameters for Flow-based Neural Posterior Estimation [90.21090932619695]
  Inferring the parameters of a model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e., when distinct sets of parameters yield identical observations. We present a method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters.
  arXiv  Detail & Related papers  (2021-02-12T12:23:13Z)
• Probing the topological Anderson transition with quantum walks [48.7576911714538]
  We consider one-dimensional quantum walks in optical linear networks with synthetically introduced disorder and tunable system parameters. The option to directly monitor the walker's probability distribution makes this optical platform ideally suited for the experimental observation of the unique signatures of the one-dimensional topological Anderson transition.
  arXiv  Detail & Related papers  (2021-02-01T21:19:15Z)

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.