Conditions for entanglement in spin systems and for multipartite entanglement
Item
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Title
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Conditions for entanglement in spin systems and for multipartite entanglement
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Identifier
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d_2009_2013:0f0140360d28:11226
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identifier
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11593
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Creator
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Zheng, Hongjun,
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Contributor
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Mark Hillery
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Date
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2012
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Language
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English
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Publisher
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City University of New York.
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Subject
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Quantum physics | Conditions | Multipartite Entanglement | Quantum Entanglement | Spin Systems
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Abstract
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This dissertation reports a series of studies of conditions for entanglement in spin systems and multipartite entanglement.;There have been numerous studies of entanglement in spin systems. These have usually focused on examining the entanglement between individual spins or determining whether the state of the system is completely separable. Here we present conditions that allow us to determine whether blocks of spins are entangled. We show that sometime these conditions can detect entanglement better than conditions involving individual spins. We apply these conditions to study entanglement in spin wave states, both when there are only a few magnons present and also at finite temperature.;We introduce two entanglement conditions that take the form of inequalities involving expectation values of operators. These conditions are sufficient conditions for entanglement that is if they are satisfied the state is entangled, but if they are not, one can say nothing about the entanglement of the state. These conditions are quite flexible, because the operators in them are not specified, and they are particularly useful in detecting multipartite entanglement.;We explore the range of utility of these conditions by considering a number of examples of entangled states, and seeing under what conditions entanglement in them can be detected by the inequalities presented here. We explore the possibility of using quantum walks on graphs to find extra edges on a graph. We focus our attention on star graph, whose edges are like spokes coming out of a central hub. If there are N spokes, we show that a quantum walk can find an extra edge connecting two of the spokes or a spoke with a loop on it in O( N ) steps.
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Type
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dissertation
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Source
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2009_2013.csv
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degree
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Ph.D.
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Program
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Physics
