Sammanfattning

Many applications of quantum mechanics depend on how the geometry of some space of quantum states alters the state's evolution.Mixed states are common in applications and their evolution is thus of interest.The Sjöqvist metric [Phys. Rev. Research 2, 013344 (2020)] describes how a mixed state evolves and has before been used to analyse the path on which a mixed two-dimensional state evolves along.In this thesis, we will use the Sjöqvist metric to find the Lagrangian governing the evolution of a mixed three-dimensional state along the shortest path and discuss the non-trivial singularities introduced by the metric, which may span some hyper-surface in an eight-dimensional space, and the similarity to black holes.

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