Optimal waveform estimation for classical and quantum systems via time-symmetric smoothing

Abstract

Classical and quantum theories of time-symmetric smoothing, which can be used to optimally estimate waveforms in classical and quantum systems, are derived using a discrete-time approach, and the similarities between the two theories are emphasized. Application of the quantum theory to homodyne phase-locked loop design for phase estimation with narrowband squeezed optical beams is studied. The relation between the proposed theory and Aharonov et al.'s weak value theory is also explored.

13 pages, 5 figures, v2: changed the title to a more descriptive one, corrected a minor mistake in Sec. IV, accepted by Physical Review A

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• General criteria for quantum state smoothing with necessary and sufficient criteria for linear Gaussian quantum systems
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• Linear Gaussian Quantum State Smoothing: Understanding the optimal unravelings for Alice to estimate Bob's state
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• How to estimate past measurement interventions on a quantum system undergoing continuous monitoring
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