Geometry of quantum evolution for mixed quantum states

Understand

The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers.

• In this work we discuss a geometric formulation of mixed quantum states represented by density operators.
• Our formulation is based on principal fiber bundles and purifications of quantum states.
• In our construction, the Riemannian metric and symplectic form on the total space are induced from the real and imaginary parts of the Hilbert-Schmidt Hermitian inner product, and we define a mechanical connection in terms of a locked inertia tensor and moment map.