Information geometry of density matrices and state estimation

Details Information geometry of density matrices and state estimation Information geometry of density matrices and state estimation

2010-09-06

arxiv.org/abs/1009.1115v2

J.Phys.A44:252002,2011

Physics

Quantum Physics

published version

Scientific paper

10.1088/1751-8113/44/25/252002

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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