On the curvature of the space of qubits

Tom 73 / 2006

Attila Andai Banach Center Publications 73 (2006), 35-48 MSC: Primary 53C20; Secondary 81Q99. DOI: 10.4064/bc73-0-2


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.


  • Attila AndaiDepartment for Mathematical Analysis,
    Budapest University of Technology and Economics
    Egry J. u. 1, 1111 Budapest, Hungary

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