A STUDY ON QUANTUM ENTANGLEMENT

Abstract

In this thesis, we focus on the problems of quantum entanglement, which is one of the most important phenomena in quantum physics. In particular, we study the quantum entanglement problem and the quantum distillation problem. Although the quantum entanglement problem is regarded as an NP-hard problem, we try to solve this problem for some subclasses of quantum states. Specifically, we introduce a new definition and SPPT states in the arbitrary multipartite system, which shows better properties then the previous one. Moreover, we introduce the completely symmetric states in the multipartite symmetric system, where the separability problem is solved for some low-rank states. Besides, we establish the relation between the separability of multi-qubit symmetric states and the Vandermonde decomposition. The distillability problem is also solved for a certain case.