Connections and Metrics Respecting Standard Purification

Details Connections and Metrics Respecting Standard Purification Connections and Metrics Respecting Standard Purification

1998-06-08

arxiv.org/abs/quant-ph/9806028v1

J.Math.Phys. 40 (1999) 3246-3267

Physics

Quantum Physics

Latex, 27 pages

Scientific paper

10.1063/1.532884

Standard purification interlaces Hermitian and Riemannian metrics on the space of density operators with metrics and connections on the purifying Hilbert-Schmidt space. We discuss connections and metrics which are well adopted to purification, and present a selected set of relations between them. A connection, as well as a metric on state space, can be obtained from a metric on the purification space. We include a condition, with which this correspondence becomes one-to-one. Our methods are borrowed from elementary *-representation and fibre space theory. We lift, as an example, solutions of a von Neumann equation, write down holonomy invariants for cyclic ones, and ``add noise'' to a curve of pure states.

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