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Quantum conditional expectations


The conditional expectation is an essential concept in probability theory and a basic tool in Bayesian estimation, as it allows one to infer hidden variables from observations in an optimal sense. Many have tried to generalize the concept for quantum mechanics, but the literature on the subject remains fragmented, confusing, and controversial. This talk presents a formalism of generalized conditional expectations that unifies most of the previous approaches. I also show how a certain version of the generalized conditional expectation can be useful for the study of quantum estimation. For example, it leads to a quantum Rao-Blackwell theorem, which may be used to improve the design of a quantum sensor in the same way the classical theorem can improve an estimator. This talk is based on Tsang, Phys. Rev. A 105, 042213 (2022) and arXiv:2212.13162 (accepted by Quantum, 2023).

Host: Aephraim Steinberg
Event series  CQIQC SeminarsQO/AMO Seminars