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.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/43495 |
| Date | 07 January 2014 |
| Creators | Cui, Wei |
| Contributors | Lo, Hoi-Kwong |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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