A smoothing theory for open quantum systems: The least mean square approach

Abstract

Unlike the classical smoothing theory, it is well known that quantum smoothers are, in general, not well--defined by the quantum conditional expectation. The purpose of this paper is to propose a new quantum smoothing theory based on the least mean squared errors. The least mean square estimate of quantum physical quantity composes from symmetric part and skew part, and we developed the recursive equations, respectively.

arXiv comment6 pages. See also Ohki "An invitation to quantum filtering and smoothing theory based on two inner products," RIMS Kokyuroku, No. 2018, pp. 18-44 (2017), (http://hdl.handle.net/2433/231710), as a reference

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• Unifying theory of quantum state estimation using past and future information
• Quantum State Smoothing for Linear Gaussian Systems
• Quantum state smoothing as an optimal estimation problem with three different cost functions
• Operational meanings of a generalized conditional expectation in quantum metrology
• Linear Gaussian Quantum State Smoothing: Understanding the optimal unravelings for Alice to estimate Bob's state