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arXiv · 1612.06410

Geometric characterization of mixed quantum states

Hoshang Heydari
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Abstract

Characterization of mixed quantum states represented by density operator is one of the most important task in quantum information processing. In this work we will present a geometric approach to characterize the density operator in terms of fiber bundle over a quantum phase space. The geometrical structure of the quantum phase space of an isospectral mixed quantum states can be realized as a co-adjoint orbit of a Lie group equipped with a specific K\"{a}hler structure. In particular we will briefly discuss the construction of a fiber bundle over the quantum phase space based on symplectic reduction and purification method. We will also show that the map is a Riemannian submersion which enable us to provide some applications of the geometric framework such as geometric phase and quantum speed limit.

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Hoshang Heydari. 2016-12-19. Geometric characterization of mixed quantum states. https://arxiv.org/abs/1612.06410

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