Entanglement, non-locality and quantum information theory

In this dissertation, motivated both by our incomplete physical understanding, and by quantum information theory, we investigate quantum non-locality. In Chapter 2, we ask the question, which quantum states are non-local? We show that any entangled pure state is non-local, but that things are complicated with mixed states. In particular, following Werner’s local hidden variable model for projective measurements on a class of entangled states, we write down an extended model that works for arbitrary positive operator valued measurements performed by the separated observers. We also show that the existence of such a model for one particular quantum state implies the existence of a similar model for a wide class of other quantum states. Finally, we discuss the fact that some quantum states display a hidden non-locality, and describe a general classification scheme for the non-locality of quantum states. In Chapter 3, we turn to a particular protocol of quantum information theory, namely, quantum teleportation. We discuss the connections between quantum teleportation and non-locality. We drive a Bell-type inequality pertaining to the teleportation scenario and investigate when it is violated. We give an example of a situation in which a teleportation fidelity of ¾ is achieved without non-locality, even though this is greater than the classical limit of 2/3. In Chapter 4, we describe the experiments that have been performed as tests of quantum non-locality and the associated loopholes. We point out an assumption, the no-memory assumption that is common to nearly all analyses of Bell-type experiments, yet is not implied by locality. We remove the assumption and give a new analysis of the ideal case.EThOS - Electronic Theses Online ServiceGBUnited Kingdo