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

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...

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Bibliographic Details
Published in:Physical review letters 2003-08, Vol.91 (9), p.090405-090405, Article 090405
Main Authors: Ericsson, Marie, Pati, Arun K, Sjöqvist, Erik, Brännlund, Johan, Oi, Daniel K L
Format: Article
Language:English
Subjects:
Fysik
Geometric phase
mixed quantum states
NATURAL SCIENCES
NATURVETENSKAP
Physics
Uhlmann holonomy
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Summary: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.
ISSN:0031-9007
1079-7114
1079-7114
DOI:10.1103/PhysRevLett.91.090405