Quantum entanglement transformations via local operations and classical communication

The primary goals of this thesis are two-fold: i) calculating the optimal entanglement transformation rate between two multipartite pure states via stochastic local operations and classical communication (SLOCC), and ii) showing the properties of a common resource for a set of multi-partite pure state via local operations and classical communication (LOCC) or SLOCC. We introduce a notion of entanglement transformation rate to characterize the asymptotic comparability of two multi-partite pure entangled states under SLOCC. For two well known SLOCC inequivalent three-qubit states: Greenberger-Horne-Zeilinger (GHZ) state and W state, we show that the entanglement transformation rate from GHZ state to W state is exactly 1. We then apply similar techniques to obtain a lower bound on the entanglement transformation rates from an N-partite GHZ state to a class of Dicke states. Then, we discuss the common resource for a set of pure states. We have completely solved the bipartite pure states case by explicitly constructing a unique optimal common resource state for any given set of states via LOCC. In the multi-partite setting, the general problem becomes quite complicated, and we focus on finding non-trivial common resources for the whole multi-partite state space of given dimensions. We show that |GHZ₃〉 = (1/√3|) (|000〉+|111〉+|222〉) is a nontrivial common resource for three-qubit systems via LOCC. We also obtain a number of interesting properties of non-trivial common resource states for two N-qubit pure states and multi-partite systems via SLOCC.

Author dc:creator

• Guo, C

• Stochastic local operations and classical communication (SLOCC).
• Quantum entanglement transformations.
• Entanglement transformation rate.
• Asymptotic comparability.

Statement dc:rights

• au.edu.uts.lib/ppc
• The author owns the copyright in this thesis including all reproduction and reuse rights for the work. The work may not be altered without the permission of the copyright owner. Attribution is essential when quoting or paraphrasing from this thesis.
• info:eu-repo/semantics/openAccess

Language dc:language.iso

en_AU

Handle dc:identifier.uri

http://hdl.handle.net/10453/39166

OAI identifier oai:identifier

oai:opus.lib.uts.edu.au:10453/39166