Multipartite Entangled States: Transformations, Entanglement Monotones, and Applications

by Wei Cui

Institution: University of Toronto
Year: 2014
Keywords: Multipartite entanglement; W-type state; Random distillation
Record ID: 2049382
Full text PDF: http://hdl.handle.net/1807/43495


Entanglement is one of the fundamental features of quantum information science. Though bipartite entanglement has been analyzed thoroughly in theory and shown to be an important resource in quantum computation and communication protocols, the theory of entanglement shared between more than two parties, which is called multipartite entanglement, is still not complete. Specifically, the classification of multipartite entanglement and the transformation property between different multipartite states by local operators and classical communications (LOCC) are two fundamental questions in the theory of multipartite entanglement. In this thesis, we present results related to the LOCC transformation between multipartite entangled states. Firstly, we investigate the bounds on the LOCC transformation probability between multipartite states, especially the GHZ class states. By analyzing the involvement of 3-tangle and other entanglement measures under weak two-outcome measurement, we derive explicit upper and lower bound on the transformation probability between GHZ class states. After that, we also analyze the transformation between N-party W type states, which is a special class of multipartite entangled states that has an explicit unique expression and a set of analytical entanglement monotones. We present a necessary and sufficient condition for a known upper bound of transformation probability between two N-party W type states to be achieved. We also further investigate a novel entanglement transformation protocol, the random distillation, which transforms multipartite entanglement into bipartite entanglement ii shared by a non-deterministic pair of parties. We find upper bounds for the random distillation protocol for general N-party W type states and find the condition for the upper bounds to be achieved. What is surprising is that the upper bounds correspond to entanglement monotones that can be increased by Separable Operators (SEP), which gives the first set of analytical entanglement monotones that can be increased by SEP. Finally, we investigate the idea of a new class of multipartite entangled states, the Absolutely Maximal Entangled (AME) states, which is characterized by the fact that any bipartition of the states would give a maximal entangled state between the two sets. The relationship between AME states and Quantum secret sharing (QSS) protocols is exhibited and the application of AME states in novel quantum communication protocols is also explored.