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

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

2002-06-11

arxiv.org/abs/quant-ph/0206063v2

Phys. Rev. Lett. 91, 090405 (2003)

Physics

Quantum Physics

minor changes, journal reference added

Scientific paper

10.1103/PhysRevLett.91.090405

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 not only depends on the geometry of the path of the system alone but also on a constrained bi-local 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 uni-local transformations and is therefore essentially a property of the system alone.

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