The Metric of Bures and the Geometric Phase

  • Armin Uhlmann
Part of the Mathematical Physics Studies book series (MPST, volume 13)


After the appearance of the papers of Berry [1], Simon [2], and of Wilczek and Zee [3], I tried to understand [4], whether there is a reasonable extension of the geometric phase - or, more accurately, of the accompanying phase factor - for general (mixed) states. A known recipe for such exercises is to use purifications: One looks for larger, possibly fictitious, quantum systems from which the original mixed states are seen as reductions of pure states. For density operators there is a standard way to do so by the use of Hilbert Schmidt operators (or by Hilbert Schmidt maps from an auxiliary Hilbert space into the original one).


Density Matrice Density Operator Geometric Phase Parallel Transport Hilbert Schmidt Operator 
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Copyright information

© Springer Science+Business Media Dordrecht 1992

Authors and Affiliations

  • Armin Uhlmann
    • 1
  1. 1.Dept. of PhysicsUniversity of LeipzigGermany

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