2015/02/11 by Douglas Farenick, Farenick, Douglas, Michael J. Kozdron +3
Mathematics · Physics and Astronomy · #28B05 #46G10 #47A10 #81P15 #FOS: Mathematics #FOS: Physical sciences #Operator Algebras (math.OA) #Probability (math.PR) #Quantum Physics (quant-ph) #math.OA #math.PR #msc:28B05 #msc:46G10 #msc:47A10 #msc:81P15 #quant-ph
paper · pdf · doi:10.48550/arxiv.1502.03213
v2: 16 pages, 0 figures, new Section 6 added
arxiv created 2015/10/06 · arxiv updated 2015/10/07
We study essentially bounded quantum random variables and show that the Gelfand spectrum of such a quantum random variable coincides with the hypoconvex hull of its essential range. 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.