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arXiv:quant-ph/0612072

Entanglement Distillation; A Discourse on Bound Entanglement in Quantum Information Theory

Lieven Clarisse

Published Dec 10, 2006• 14 citations
arXivHTMLPDF

Abstract

PhD thesis (University of York). The thesis covers in a unified way the material presented in quant-ph/0403073, quant-ph/0502040, quant-ph/0504160, quant-ph/0510035, quant-ph/0512012 and quant-ph/0603283. It includes two large review chapters on entanglement and distillation.
DOI
10.48550/arxiv.quant-ph/0612072

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Abstract An entangled state is bound entangled if one cannot combine any number of copies of the state to a maximally entangled state by using only local operations and classical communication. If one formalizes this notion of bound entanglement, one arrives immediately at four different definitions. In addition, at least three more definitions are commonly used in the literature, in particular in the very first paper on bound entanglement. Here we review critical distillation protocols and we examine how different results from quantum information theory interact in order to prove that all seven definitions are eventually equivalent. Our self-contained analysis unifies and extends previous results scattered in the literature and reveals details of the structure of bound entanglement.
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This report provides a brief review of recently developed extended framework for fundamental physics, designated as Quantum Field Mechanics and including causally complete and intrinsically unified theory of explicitly emerging elementary particles, their inherent properties, quantum and relativistic behaviour, interactions and their results. Essential progress with respect to usual theory is attained due to the unreduced, nonperturbative analysis of arbitrary interaction process revealing a qualitatively new phenomenon of dynamic multivaluedness of interaction results and their dynamically entangled structure giving rise to universally defined dynamic complexity (physics/9806002) and absent in usual, always perturbative and dynamically single-valued models with the zero value of unreduced complexity (including substitutes used for "complexity", "chaoticity", "self-organisation", etc.). It is shown how the observed world structure, starting from elementary particles and their interactions, dynamically emerges from the unreduced interaction between two initially homogeneous, physically real protofields (quant-ph/9902015, quant-ph/9902016). In that way one avoids arbitrary imposition of abstract entities and unprovable postulates or "principles", let alone "mysteries", of conventional theory, which now obtain unified, consistent and realistic explanation in terms of unreduced dynamic complexity. We complete the description of fundamental world structure emergence and properties by an outline of experimental implications and resulting causally substantiated change of research strategy.