10.1007/s10955-008-9576-1
Reimann, Peter
Peter
Reimann
Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure
SPRINGER
2008
2010-04-26T09:43:38Z
2018-07-24T12:58:38Z
journal_article
https://pub.uni-bielefeld.de/record/1586626
https://pub.uni-bielefeld.de/record/1586626.json
Consider a mixed quantum mechanical state, describing a statistical ensemble in terms of an arbitrary density operator rho of low purity, tr rho(2) << 1, and yielding the ensemble averaged expectation value tr(rho A) for any observable A. Assuming that the given statistical ensemble rho is generated by randomly sampling pure states vertical bar psi > according to the corresponding so-called Gaussian adjusted projected measure (Goldstein et al. in J. Stat. Phys. 125:1197, 2006), the expectation value <psi vertical bar A vertical bar psi > is shown to be extremely close to the ensemble average tr(rho A) for the overwhelming majority of pure states vertical bar psi > and any experimentally realistic observable A. In particular, such a 'typicality' property holds whenever the Hilbert space H of the system contains a high dimensional subspace H+ subset of H with the property that all vertical bar psi > epsilon H+ are realized with equal probability and all other vertical bar psi > epsilon H are excluded.