Quantum State Smoothing

Abstract

Smoothing is an estimation method whereby a classical state (probability distribution for classical variables) at a given time is conditioned on all-time (both past and future) observations. Here we define a smoothed quantum state for a partially monitored open quantum system, conditioned on an all-time monitoring-derived record. We calculate the smoothed distribution for a hypothetical unobserved record which, when added to the real record, would complete the monitoring, yielding a pure-state "quantum trajectory". Averaging the pure state over this smoothed distribution yields the (mixed) smoothed quantum state. We study how the choice of actual unravelling affects the purity increase over that of the conventional (filtered) state conditioned only on the past record.

Updated to its last version (5 pages+5 pages (SM))

References in corpus (9)

• Quantum feedback control of a superconducting qubit: Persistent Rabi oscillations
• Quantum-enhanced optical phase tracking
• Mapping the optimal route between two quantum states
• Quantum Imaging beyond the Diffraction Limit by Optical Centroid Measurements
• Time-Symmetric Quantum Theory of Smoothing
• Prediction and retrodiction for a continuously monitored superconducting qubit
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• Fundamental quantum limits to waveform detection
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Cited by in corpus (55)

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• Quantum Trajectory Thermodynamics with Discrete Feedback Control
• Conditional past-future correlation induced by non-Markovian dephasing reservoirs
• Spikes in quantum trajectories
• Quantum state tomography with non-instantaneous measurements, imperfections and decoherence
• Homodyne monitoring of post-selected decay
• Retrodiction beyond the Heisenberg uncertainty relation
• Optimal Pure-State Qubit Tomography via Sequential Weak Measurements
• Unifying theory of quantum state estimation using past and future information
• Driving quantum systems with repeated conditional measurements
• Quantum State Smoothing for Linear Gaussian Systems
• Measuring Fluorescence to Track a Quantum Emitter's State: A Theory Review
• Adaptive measurement filter: efficient strategy for optimal estimation of quantum Markov chains
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• Quantum state smoothing: Why the types of observed and unobserved measurements matter
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• Exact quantum Bayesian rule for qubit measurements in circuit QED
• Past observable dynamics of a continuously monitored qubit
• Volterra filters for quantum estimation and detection
• Smoothed quantum-classical states in time-irreversible hybrid dynamics
• Quantum state smoothing as an optimal estimation problem with three different cost functions
• General criteria for quantum state smoothing with necessary and sufficient criteria for linear Gaussian quantum systems
• A smoothing theory for open quantum systems: The least mean square approach
• Quantum proportional-integral (PI) control
• Operational meanings of a generalized conditional expectation in quantum metrology
• Quantum Bayes' rule and Petz transpose map from the minimum change principle
• Linear Gaussian Quantum State Smoothing: Understanding the optimal unravelings for Alice to estimate Bob's state
• Quantum retrodiction in Gaussian systems and applications in optomechanics
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• Conditioned spin and charge dynamics of a single electron quantum dot
• Entropic relations for retrodicted quantum measurements
• Gradual partial-collapse theory for ideal nondemolition measurements of qubits in circuit QED
• Quantum-classical hybrid dynamics: coupling mechanisms and diffusive approximation
• Tomography of an optomechanical oscillator via parametrically amplified position measurement
• Quantum state smoothing cannot be assumed classical even when the filtering and retrofiltering are classical
• Loschmidt echo and scrambling of systematic errors in tomography -- a quantum signature of chaos
• Inequivalent ways to apply semi-classical smoothing to a quantum system
• Completely positive trace-preserving maps for higher-order unraveling of Lindblad master equations
• Estimating quantum Markov chains using coherent absorber post-processing and pattern counting estimator
• Proper and improper mixed states serve as different prior beliefs for quantum state retrodiction
• A Retrodictive Approach to Quantum State Smoothing
• Generalized conditional expectations for quantum retrodiction and smoothing
• Measuring the time atoms spend in the excited state due to a photon they don't absorb
• Prediction-retrodiction measurements for teleportation and conditional state transfer
• Quantum state smoothing when Alice assumes the wrong type of monitoring by Bob
• Quantum backaction effects in sequential measurements
• Counterfactual quantum measurements
• Quantum thermodynamics under continuous monitoring: a general framework
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