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Characterizing entanglement in quantum information

Citation

Spedalieri, Federico Maximiliano (2003) Characterizing entanglement in quantum information. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-05222003-121058

Abstract

Entanglement is a key resource in the emerging field of Quantum Information. The strong correlations between systems described by an entangled state allow us to perform certain tasks more efficiently than it would be possible by using only classical resources. This is why the characterization of entanglement is one of the most important problems in Quantum Information.

In this thesis, we analyze several aspects of entanglement. First, we introduce a new family of criteria to determine if a bipartite mixed state is entangled or not. This family consists of a sequence of tests that can be implemented efficiently, and has the property that all entangled states can be detected by some test in the sequence.

Each test in the family can be stated as a semidefinite program, which is a class of convex optimization problems. The duality structure of these programs allows us to explicitly construct an entanglement witness that proves entanglement of a state, whenever the state fails one of the tests in the sequence. The entanglement witnesses constructed in this manner have well-defined algebraic properties that can be used to give a characterization of the interior of the set of all possible entanglement witnesses, as well as the set of strictly positive bihermitian forms and the set of strictly positive maps.

We also study deterministic transformations of three-qubit pure state when only local operations and classical communication (LOCC) are allowed. We derive strong constraints that the operations and states involved must satisfy, and we apply these results to characterize the set of real states that can be obtained from the GHZ state by LOCC.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:entanglement; entanglement manipulation; entanglement witnesses; positive forms; positive maps; positive maps; semidefinite programs; separability; separability criteria; separable states; three-qubit pure states
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Preskill, John P.
Thesis Committee:
  • Preskill, John P. (chair)
  • Schumacher, Benjamin
  • Peck, Charles W.
  • Mabuchi, Hideo
Defense Date:19 May 2003
Record Number:CaltechETD:etd-05222003-121058
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-05222003-121058
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1937
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:22 May 2003
Last Modified:26 Dec 2012 02:44

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