On the curvature of the space of qubits

Attila Andai. "On the curvature of the space of qubits." Banach Center Publications 73.1 (2006): 35-48. <http://eudml.org/doc/281986>.

@article{AttilaAndai2006,
abstract = {The Fisher informational metric is unique in some sense (it is the only Markovian monotone distance) in the classical case. A family of Riemannian metrics is called monotone if its members are decreasing under stochastic mappings. These are the metrics to play the role of Fisher metric in the quantum case. Monotone metrics can be labeled by special operator monotone functions, according to Petz's Classification Theorem. The aim of this paper is to present an idea how one can narrow the set of monotone metrics from the statistical point of view, and to show that the monotone metrics which occur in the literature most often fit to this idea in qubit case.},
author = {Attila Andai},
journal = {Banach Center Publications},
keywords = {state space; monotone statistical metrics; scalar curvature; Fisher informational; monotone metrics},
language = {eng},
number = {1},
pages = {35-48},
title = {On the curvature of the space of qubits},
url = {http://eudml.org/doc/281986},
volume = {73},
year = {2006},
}

TY - JOUR
AU - Attila Andai
TI - On the curvature of the space of qubits
JO - Banach Center Publications
PY - 2006
VL - 73
IS - 1
SP - 35
EP - 48
AB - The Fisher informational metric is unique in some sense (it is the only Markovian monotone distance) in the classical case. A family of Riemannian metrics is called monotone if its members are decreasing under stochastic mappings. These are the metrics to play the role of Fisher metric in the quantum case. Monotone metrics can be labeled by special operator monotone functions, according to Petz's Classification Theorem. The aim of this paper is to present an idea how one can narrow the set of monotone metrics from the statistical point of view, and to show that the monotone metrics which occur in the literature most often fit to this idea in qubit case.
LA - eng
KW - state space; monotone statistical metrics; scalar curvature; Fisher informational; monotone metrics
UR - http://eudml.org/doc/281986
ER -