Aspects of entanglement

grantor: University of TorontoWe present a theoretical study of entanglement in selected topics from quantum cryptography, Bose-Einstein condensation and the interpretation of quantum mechanics. First, we consider the two-party cryptographic task known as bit commitment. For specific types of bit commitment protocols, we determine the optimal cheating strategy for one of the parties, and identify the cases wherein the cheater must have the ability to generate entanglement. We proceed to determine the maximum degree of security that can be achieved against each party given various restrictions on the form of the protocol. In particular, we identify a family of protocols wherein there is a linear trade-off between the maximum probabilities of each party cheating successfully. Next, we consider the fragmentation of a Bose-Einstein condensate, wherein multiple single-particle wavefunctions acquire a macroscopic occupation number. We demonstrate that for atoms with weak repulsive inter-particle interactions trapped in a double-well potential, one can achieve various degrees of squeezing in the relative number of atoms between the wells by varying the height of the central barrier and allowing the system to relax to the ground state. This constitutes a technique for generating entanglement between a pair of localized atomic modes. Finally, we propose a modal interpretation of quantum mechanics based on a novel choice of preferred decomposition for a multi-partite entangled state: from among all decompositions containing only product states, it is the one for which the coefficients squared have the smallest Shannon entropy. This proposal is shown to compare favorably with those that make use of the bi-orthogonal decomposition, particularly in the extent to which it provides a solution to the quantum measurement problem.Ph.D