@inproceedings{5a4ad96be360419f9a997afc56f9ab08,
title = "A quantum mechanical version of price's theorem for Gaussian states",
abstract = "This paper is concerned with integro-differential identities which are known in statistical signal processing as Price's theorem for expectations of nonlinear functions of jointly Gaussian random variables. We revisit these relations for classical variables by using the Frechet differentiation with respect to covariance matrices, and then show that Price's theorem carries over to a quantum mechanical setting. The quantum counterpart of the theorem is established for Gaussian quantum states in the framework of the Weyl functional calculus for quantum variables satisfying the Heisenberg canonical commutation relations. The quantum mechanical version of Price's theorem relates the Frechet derivative of the generalized moment of such variables with respect to the real part of their quantum covariance matrix with other moments. As an illustrative example, we consider these relations for quadratic-exponential moments which are relevant to risk-sensitive quantum control.",
keywords = "Gaussian quantum state, Price's theorem, Weyl quantization, canonical commutation relations, generalized moment, integro-differential identity, quadratic-exponential moment, quantum variables",
author = "Vladimirov, {Igor G.}",
note = "Publisher Copyright: {\textcopyright} 2014 Engineers Australia.; 4th Australian Control Conference, AUCC 2014 ; Conference date: 17-11-2014 Through 18-11-2014",
year = "2015",
month = dec,
day = "16",
doi = "10.1109/AUCC.2014.7358675",
language = "English",
series = "Proceedings of 2014 Australian Control Conference, AUCC 2014",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "118--123",
booktitle = "Proceedings of 2014 Australian Control Conference, AUCC 2014",
address = "United States",
}