Mixed state geometric phases, entangled systems, and local unitary transformations

M Ericsson, A K Pati, E Sjoqvist, J Brannlund, D K L Oi

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The geometric phase for a pure quantal state undergoing an arbitrary evolution is a "memory" of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution depends not only on the geometry of the path of the system alone but also on a constrained bilocal unitary evolution of the purified entangled state. We analyze this in general, illustrate it for the qubit case, and propose an experiment to test this effect. We also show that the mixed state geometric phase proposed recently in the context of interferometry requires unilocal transformations and is therefore essentially a property of the system alone.

Original languageEnglish
Article number090405
Pages (from-to)-
Number of pages4
JournalPhysical Review Letters
Issue number9
Publication statusPublished - 29 Aug 2003


  • quantum systems
  • parallel transport
  • interferometry

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