Theoretical Study On Transformation Of Quantum Entangled States

The rapid development of quantum information processing has led us to view entanglement as a crucial physical resource. Research on the properties of entanglements can help us to manipulate and control it better, thereby exploring more applications of it. The theory of entanglement transformation mostly aims at uncovering the laws of transformation via LOCC between different entanglements. These laws are important since many applications of quantum information (e.g. quantum cryptography, quantum superdense coding, and quantum teleportation) involve spatially separate parties who must manipulate an entangled state without performing joint operations.This article focuses on the study of conditions and procedures for entanglement transformation. The main contents are as follows:We first present the basic conceptions of quantum entanglement, quantum operation and entanglement transformation, then briefly introduce the typical applications of entanglement in quantum information, finally demonstrate the main results on the study of entanglement's properties, including the distinguishability, distillation and transformation of entanglements.After introducing the necessary and sufficient condition of entanglement transformation of bipartite pure states, an explicit procedure for achieving the transformation is presented. Our procedure is much simper than the previous ones in the sense that, it only involves two steps and the explicit expression of local general measurement used in the procedure can be obtained by solving a set of linear equations. Furthermore, this procedure is still applicable in high dimensional case.We investigate the laws of distilling GHZ states from multiple copies of arbitrary W-class state. We first show that, with a supply of two copies of arbitrary W-class state, we can always construct an explicit procedure to distill a GHZ state with a nonzero probability. Then based on this result, a simple procedure for distilling GHZ state from n copies of arbitrary W-class state is presented.