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Entanglement of Multipartite Quantum States and the Generalized Quantum Search


Gingrich, Robert Michael (2002) Entanglement of Multipartite Quantum States and the Generalized Quantum Search. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/0M1P-NS54.


In chapter 2 various parameterizations for the orbits under local unitary transformations of three-qubit pure states are analyzed. It is shown that the entanglement monotones of any multipartite pure state uniquely determine the orbit of that state. It follows that there must be an entanglement monotone for three-qubit pure states which depends on the Kempe invariant defined in [1]. A form for such an entanglement monotone is proposed. A theorem is proved that significantly reduces the number of entanglement monotones that must be looked at to find the maximal probability of transforming one multipartite state to another.

In chapter 3 Grover's unstructured quantum search algorithm is generalized to use an arbitrary starting superposition and an arbitrary unitary matrix. A formula for the probability of the generalized Grover's algorithm succeeding after n iterations is derived. This formula is used to determine the optimal strategy for using the unstructured quantum search algorithm. The speedup obtained illustrates that a hybrid use of quantum computing and classical computing techniques can yield a performance that is better than either alone. The analysis is extended to the case of a society of k quantum searches acting in parallel.

In chapter 4 the positive map Г : p → (Trρ) - ρ is introduced as a separability criterion. Any separable state is mapped by the tensor product of Г and the identity in to a non-negative operator, which provides a necessary condition for separability. If Г acts on a two-dimensional subsystem, then it is equivalent to partial transposition and therefore also sufficient for 2 x 2 and 2 x 3 systems. Finally, a connection between this map for two qubits and complex conjugation in the "magic" basis [2] is displayed.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Physics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Minor Option:Computer Science
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Preskill, John P.
Thesis Committee:
  • Preskill, John P. (chair)
  • Adami, Christoph Carl
  • Frautschi, Steven C.
  • Mabuchi, Hideo
Defense Date:23 August 2001
Record Number:CaltechTHESIS:01202012-104927686
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6769
Deposited By: Benjamin Perez
Deposited On:23 Jan 2012 19:34
Last Modified:05 Nov 2021 20:09

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