Quantum State Smoothing for Linear Gaussian Systems

Abstract

Quantum state smoothing is a technique for assigning a valid quantum state to a partially observed dynamical system, using measurement records both prior and posterior to an estimation time. We show that the technique is greatly simplified for Linear Gaussian quantum systems, which have wide physical applicability. We derive a closed-form solution for the quantum smoothed state, which is more pure than the standard filtered state, whilst still being described by a physical quantum state, unlike other proposed quantum smoothing techniques. We apply the theory to an on-threshold optical parametric oscillator, exploring optimal conditions for purity recovery by smoothing. The role of quantum efficiency is elucidated, in both low and high efficiency limits.

6 pages, 3 figures, 5 pages Supplemental Material. The red text indicates changes following the Erratum Phys. Rev. Lett. 122, 190402 (2019)

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• Quantum state smoothing: Why the types of observed and unobserved measurements matter
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• Limits to Perception by Quantum Monitoring with Finite Efficiency
• Inequivalent ways to apply semi-classical smoothing to a quantum system
• A Retrodictive Approach to Quantum State Smoothing