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Title: Cumulants and the moment algebra: Tools for analyzing weak measurements

Abstract

Recently it has been shown that cumulants significantly simplify the analysis of multipartite weak measurements. Here we consider the mathematical structure that underlies this and find that it can be formulated in terms of what we call the moment algebra. Apart from resulting in simpler proofs, the flexibility of this structure allows generalizations of the original results to a number of weak measurement scenarios, including one where the weakly interacting pointers reach thermal equilibrium with the probed system.

Authors:
 [1];  [2]
  1. Institute for Theoretical Physics, ETH Zurich, 8093 Zurich (Switzerland)
  2. Centre for Quantum Computation, DAMTP, University of Cambridge, Cambridge CB3 0WA (United Kingdom)
Publication Date:
OSTI Identifier:
21294024
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 50; Journal Issue: 4; Other Information: DOI: 10.1063/1.3093270; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; HILBERT SPACE; MATHEMATICAL OPERATORS; QUANTUM MECHANICS; SET THEORY; THERMAL EQUILIBRIUM

Citation Formats

Aaberg, Johan, Communication Technology Laboratory, ETH Zurich, 8092 Zurich, and Mitchison, Graeme. Cumulants and the moment algebra: Tools for analyzing weak measurements. United States: N. p., 2009. Web. doi:10.1063/1.3093270.
Aaberg, Johan, Communication Technology Laboratory, ETH Zurich, 8092 Zurich, & Mitchison, Graeme. Cumulants and the moment algebra: Tools for analyzing weak measurements. United States. https://doi.org/10.1063/1.3093270
Aaberg, Johan, Communication Technology Laboratory, ETH Zurich, 8092 Zurich, and Mitchison, Graeme. 2009. "Cumulants and the moment algebra: Tools for analyzing weak measurements". United States. https://doi.org/10.1063/1.3093270.
@article{osti_21294024,
title = {Cumulants and the moment algebra: Tools for analyzing weak measurements},
author = {Aaberg, Johan and Communication Technology Laboratory, ETH Zurich, 8092 Zurich and Mitchison, Graeme},
abstractNote = {Recently it has been shown that cumulants significantly simplify the analysis of multipartite weak measurements. Here we consider the mathematical structure that underlies this and find that it can be formulated in terms of what we call the moment algebra. Apart from resulting in simpler proofs, the flexibility of this structure allows generalizations of the original results to a number of weak measurement scenarios, including one where the weakly interacting pointers reach thermal equilibrium with the probed system.},
doi = {10.1063/1.3093270},
url = {https://www.osti.gov/biblio/21294024}, journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 4,
volume = 50,
place = {United States},
year = {Wed Apr 15 00:00:00 EDT 2009},
month = {Wed Apr 15 00:00:00 EDT 2009}
}