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arXiv · 1009.1115

Information geometry of density matrices and state estimation

Dorje C. Brody
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Abstract

Given a pure state vector |x> and a density matrix rho, the function p(x|rho)= defines a probability density on the space of pure states parameterised by density matrices. The associated Fisher-Rao information measure is used to define a unitary invariant Riemannian metric on the space of density matrices. An alternative derivation of the metric, based on square-root density matrices and trace norms, is provided. This is applied to the problem of quantum-state estimation. In the simplest case of unitary parameter estimation, new higher-order corrections to the uncertainty relations, applicable to general mixed states, are derived.

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Dorje C. Brody. 2011-06-02. Information geometry of density matrices and state estimation. https://doi.org/10.1088/1751-8113%2F44%2F25%2F252002

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