The Scalar Curvature of the Bures Metric on the Space of Density Matrices

Details The Scalar Curvature of the Bures Metric on the Space of Density Matrices The Scalar Curvature of the Bures Metric on the Space of Density Matrices

1998-10-05

arxiv.org/abs/quant-ph/9810012v1

J.Geom.Phys. 31 (1999) 16-24

Physics

Quantum Physics

Latex, 9 pages

Scientific paper

10.1016/S0393-0440(98)00068-0

The Riemannian Bures metric on the space of (normalized) complex positive matrices is used for parameter estimation of mixed quantum states based on repeated measurements just as the Fisher information in classical statistics. It appears also in the concept of purifications of mixed states in quantum physics. Here we determine its scalar curvature and Ricci tensor and prove a lower bound for the curvature on the submanifold of trace one matrices. This bound is achieved for the maximally mixed state, a further hint for the quantum statistical meaning of the scalar curvature.

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