Mathematics – Probability
Scientific paper
2003-04-14
Mathematics
Probability
Scientific paper
In the search of appropriate riemannian metrics on quantum state space the concept of statistical monotonicity, or contraction under coarse graining, has been proposed by Chentsov. The metrics with this property have been classified by Petz. All the elements of this family of geometries can be seen as quantum analogues of Fisher information. Although there exists a number of general theorems sheding light on this subject, many natural questions, also stemming from applications, are still open. In this paper we discuss a particular member of the family, the Wigner-Yanase information. Using a well-known approach that mimics the classical pull-back approach to Fisher information, we are able to give explicit formulae for the geodesic distance, the geodesic path, the sectional and scalar curvatures associated to Wigner-Yanase information. Moreover we show that this is the only monotone metric for which such an approach is possible.
Gibilisco Paolo
Isola Tommaso
No associations
LandOfFree
Wigner-Yanase information on quantum state space:the geometric approach does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Wigner-Yanase information on quantum state space:the geometric approach, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Wigner-Yanase information on quantum state space:the geometric approach will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-548054