A geometric framework for mixed quantum states based on a Kahler structure

作者：Heydari Hoshang^*

来源：Journal of Physics A-Mathematical and Theoretical, 2015, 48(25): 255301.

DOI：10.1088/1751-8113/48/25/255301

• geometric quantum mechanics
• symeplectic geometry
• Kahler manifold
• mixed quantum states
• quantum information

In this paper we introduce a geometric framework for mixed quantum states based on a Kahler structure. The geometric framework includes a symplectic form, an almost complex structure, and a Riemannian metric that characterize the space of mixed quantum states. We argue that the almost complex structure is integrable. We also in detail discuss a visualizing application of this geometric framework by deriving a geometric uncertainty relation for mixed quantum states. The framework is computationally effective and it provides us with a better understanding of general quantum mechanical systems.

• 出版日期2015-6-26