Parameter estimation for quantum jump unraveling

Abstract

We consider the estimation of parameters encoded in the measurement record of a continuously monitored quantum system in the jump unraveling, corresponding to a single-shot scenario, where information is continuously gathered. Here, it is generally difficult to assess the precision of the estimation procedure via the Fisher Information due to intricate temporal correlations and memory effects. In this paper we provide a full set of solutions to this problem. First, for multi-channel renewal processes we relate the Fisher Information to an underlying Markov chain and derive a easily computable expression for it. For non-renewal processes, we introduce a new algorithm that combines two methods: the monitoring operator method for metrology and the Gillespie algorithm which allows for efficient sampling of a stochastic form of the Fisher Information along individual quantum trajectories. We show that this stochastic Fisher Information satisfies useful properties related to estimation on a single run. Finally, we consider the case where some information is lost in data compression/post-selection and provide tools for computing the Fisher Information in this case. All scenarios are illustrated with instructive examples from quantum optics and condensed matter.

References in corpus (42)

• Advances in Quantum Metrology
• Quantum metrology
• Quantum metrology with nonclassical states of atomic ensembles
• Quantum jumps of light recording the birth and death of a photon in a cavity
• Quantum enhanced measurements without entanglement
• Observation of quantum jumps in a superconducting artificial atom
• Thermodynamics of Quantum Jump Trajectories
• Fundamental Quantum Limit to Waveform Estimation
• Multi-parameter estimation beyond Quantum Fisher Information
• Unravelling the large deviation statistics of Markovian open quantum systems
• The Fisher information and the quantum Cramer-Rao sensitivity limit of continuous measurements
• Collisional quantum thermometry
• Bayesian parameter inference from continuously monitored quantum systems
• Stochastic Schrodinger equations
• State and dynamical parameter estimation for open quantum systems
• Violating the Thermodynamic Uncertainty Relation in the Three-Level Maser
• Restoring Heisenberg scaling in noisy quantum metrology by monitoring the environment
• Thermodynamics of Precision in Markovian Open Quantum Dynamics
• The quantum Bell-Ziv-Zakai bounds and Heisenberg limits for waveform estimation
• Efficient Quantum Filtering for Quantum Feedback Control
• Bayesian parameter estimation by continuous homodyne detection
• Estimating Temperature via Sequential Measurements
• Fisher information and asymptotic normality in system identification for quantum Markov chains
• Entanglement and thermokinetic uncertainty relations in coherent mesoscopic transport
• Coherent measurements in quantum metrology
• Quantum Estimation via Sequential Measurements
• Rapid estimation of drifting parameters in continuously measured quantum systems
• Many Roads to Synchrony: Natural Time Scales and Their Algorithms
• Fisher information of correlated stochastic processes
• Parameter estimation and system identification for continuously-observed quantum systems
• Sanov and Central Limit Theorems for output statistics of quantum Markov chains
• Adaptive measurement filter: efficient strategy for optimal estimation of quantum Markov chains
• Stochastic collisional quantum thermometry
• Quantum Jump Metrology
• Quantum renewal processes
• Unravelling Metastable Markovian Open Quantum Systems
• Probe thermometry with continuous measurements
• The best Fisher is upstream: data processing inequalities for quantum metrology
• A quantum collisional classifier driven by information reservoir
• Stochastic metrology and the empirical distribution
• Gillespie algorithm for quantum jump trajectories
• A photonic engine fueled by quantum-correlated atoms

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• Fisher information rates in sequentially measured quantum systems
• Critical Quantum Sensing: a tutorial on parameter estimation near quantum phase transitions
• Time correlations from steady-state expectation values
• Parameter estimation with one- and two-time measurements on the emission field of the boundary time crystal