Geometry of Quantum Statistical Inference

Brody, D C and Hughston, L P. 1996. Geometry of Quantum Statistical Inference. Physical Review Letters, 77(14), pp. 2851-2854. ISSN 0031-9007 [Article]

GEO_Q_stat_inf.pdf - Published Version

Download (127kB) | Preview

Abstract or Description

An efficient geometric formulation of the problem of parameter estimation is developed, based on Hilbert space geometry. This theory, which allows for a transparent transition between classical and quantum statistical inference, is then applied to the analysis of exponential families of distributions (of relevance to statistical mechanics) and quantum mechanical evolutions. The extension to quantum theory is achieved by the introduction of a complex structure on the given real Hilbert space. We find a set of higher order corrections to the parameter estimation variance lower bound, which are potentially important in quantum mechanics, where these corrections appear as modifications to Heisenberg uncertainty relations for the determination of the parameter.

Item Type:


Identification Number (DOI):

Additional Information:

©1996 American Physical Society

Departments, Centres and Research Units:



30 September 1996Published

Item ID:


Date Deposited:

08 Feb 2022 14:25

Last Modified:

08 Feb 2022 14:25

Peer Reviewed:

Yes, this version has been peer-reviewed.


View statistics for this item...

Edit Record Edit Record (login required)