Abstract
A mapping is established in connecting density matrices, associated with an evolution of a quantum open system, with vector ray in a complex projective Hilbert space. By using the corresponding vector ray to represent the open two-level system, we may observe the geometric phase for the open two-level system. The geometric phase of the open two-level system depends only on the smooth (open or closed) curve in the complex projective Hilbert space of ray, which is formulated entirely in terms of geometric structures on this space.
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