Information and metrics in Hilbert space
- 1 March 1997
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 55 (3) , 1695-1702
- https://doi.org/10.1103/physreva.55.1695
Abstract
The concept of distance in Hilbert space is relevant in a variety of scenarios, in particular for investigating the quality of different approximations. In this work we study the relations between (i) statistical distances (SD) on a probability space, on the one hand, and (ii) different metrics on Hilbert space (MHS), on the other hand. As a result, we are able to establish some universal relations between SD and MHS and to apply them to one-dimensional problems.Keywords
This publication has 28 references indexed in Scilit:
- Statistical distance and the geometry of quantum statesPhysical Review Letters, 1994
- Quantized geometry associated with uncertainty and correlationPhysical Review A, 1993
- Typical states and density matricesJournal of Geometry and Physics, 1992
- Relation between “phases” and “distance” in quantum evolutionPhysics Letters A, 1991
- Quantum fisher metric and uncertainty relationsPhysics Letters A, 1988
- Geometrical description of Berry's phasePhysical Review A, 1987
- Statistical distance and Hilbert spacePhysical Review D, 1981
- Riemannian structure on manifolds of quantum statesCommunications in Mathematical Physics, 1980
- On Unitary Ray Representations of Continuous GroupsAnnals of Mathematics, 1954
- XXI.—On the Dominance RatioProceedings of the Royal Society of Edinburgh, 1923