On asymptotic quantum statistical inference. (English) Zbl 1325.62053

Gill, Richard D.; Guţă, Mădălin

Banerjee, M. (ed.) et al., From probability to statistics and back: high-dimensional models and processes. A Festschrift in honor of Jon A. Wellner. Including papers from the conference, Seattle, WA, USA, July 28–31, 2010. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 978-0-940600-83-6). Institute of Mathematical Statistics Collections 9, 105-127 (2013).

Summary: We study asymptotically optimal statistical inference concerning the unknown state of \(N\) identical quantum systems, using two complementary approaches: a “poor man’s approach” based on the van Trees inequality, and a rather more sophisticated approach using the recently developed quantum form of LeCam’s theory of local asymptotic normality.
For the entire collection see [Zbl 1319.62002].

MSC:

62F12	Asymptotic properties of parametric estimators
62P35	Applications of statistics to physics

Keywords:

quantum Cramér-Rao bound; Van Trees inequality; local asymptotic normality; quantum local asymptotic normality