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

References in corpus (5)

• Quantum Kalman Filtering and the Heisenberg Limit in Atomic Magnetometry
• Time-Symmetric Quantum Theory of Smoothing
• Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous time limit and state-variable approach to phase-locked loop design
• Quantum theory of optical temporal phase and instantaneous frequency
• Quantum trajectories for the realistic measurement of a solid-state charge qubit