Mixed State Geometric Phases, Entangled Systems, and Local Unitary Transformations (original) (raw)
2003, Physical Review Letters
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. PACS numbers: 03.65.Vf, 42.50.Dv Pancharatnam [1] was first to introduce the concept of geometric phase in his study of interference of light in distinct states of polarization. Its quantal counterpart was discovered by Berry [2], who proved the existence of geometric phases in cyclic adiabatic evolutions. This was generalized to the case of nonadiabatic [3] and noncyclic [4] evolutions. The geometric phase was also derived on the basis of purely kinematic considerations [5].
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