Geometry and physics of entanglement

Abstract

In this thesis, the issue of quantum entanglement is studied from a geometrical perspective. We have explored the geometry of the quantum state space and relativistic space-time structure to study the condition for detecting quantum entanglement in bipartite quantum systems. The issue of entanglement is then explored in the context of quantum measurement. In all quantum measurement process, the observable to be measured is coupled to a suitable pointer degree of freedom. This coupling establishes an entanglement between state of the system and the pointer state. By reading the pointer variable we obtain information about the observable. The extent of entanglement between the pointer state and the system state then sets a limit on the amount of information that can be obtained by reading the pointer variable. We have used this concept in the analysis of the Stern-Gerlach experiment and explored the concept of coarse measurement in the quantum phase space.