Connections and Metrics Respecting Standard Purification

J. Dittmann; A. Uhlmann

doi:10.1063/1.532884

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arXiv · quant-ph/9806028

Connections and Metrics Respecting Standard Purification

J. Dittmann·A. Uhlmann

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Abstract

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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J. Dittmann, A. Uhlmann. 1998-06-08. Connections and Metrics Respecting Standard Purification. https://doi.org/10.1063/1.532884

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