Spectra and variance of quantum random variables

We study essentially bounded quantum random variables and show that the Gelfand spectrum of such a quantum random variable ψ coincides with the hypoconvex hull of the essential range of ψ. Moreover, a notion of operator-valued variance is introduced, leading to a formulation of the moment problem in...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical analysis and applications 2016-02, Vol.434 (2), p.1106-1122
Main Authors: Farenick, Douglas, Kozdron, Michael J., Plosker, Sarah
Format: Article
Language:English
Subjects:
Positive operator-valued measure
Quantum noise
Quantum probability measure
Quantum random variable
Smearing
Variance
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study essentially bounded quantum random variables and show that the Gelfand spectrum of such a quantum random variable ψ coincides with the hypoconvex hull of the essential range of ψ. Moreover, a notion of operator-valued variance is introduced, leading to a formulation of the moment problem in the context of quantum probability spaces in terms of operator-theoretic properties involving semi-invariant subspaces and spectral theory. As an application of quantum variance, new measures of random and inherent quantum noise are introduced for measurements of quantum systems, modifying some recent ideas of Polterovich [17].
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2015.09.055