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Aperiodic Univariate and Multivariate Merit Factors
 SETA’04, Sequences and their Applications, Seoul, Accepted for Proceedings of SETA04, Lecture Notes in Computer Science
, 2004
"... Abstract. Merit factor of a binary sequence is reviewed, and constructions are described that appear to satisfy an asymptotic merit factor of 6.3421... Multivariate merit factor is characterised and recursive Boolean constructions are presented which satisfy a nonvanishing asymptote in multivariate ..."
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Abstract. Merit factor of a binary sequence is reviewed, and constructions are described that appear to satisfy an asymptotic merit factor of 6.3421... Multivariate merit factor is characterised and recursive Boolean constructions are presented which satisfy a nonvanishing asymptote in multivariate merit factor. Clifford merit factor is characterised as a generalisation of multivariate merit factor and as a type of quantum merit factor. Recursive Boolean constructions are presented which, however, only satisfy an asymptotic Clifford merit factor of zero. It is demonstrated that Boolean functions obtained via quantum error correcting codes tend to maximise Clifford merit factor. Results are presented as to the distribution of the above merit factors over the set of binary sequences and Boolean functions. 1
Entanglement Distillation  A Discourse on Bound Entanglement in Quantum Information Theory
, 2006
"... In recent years entanglement has been recognised as a useful resource in quantum information and computation. This applies primarily to pure state entanglement which is, due to interaction with the environment, rarely available. Decoherence provides the main motivation for the study of entanglement ..."
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In recent years entanglement has been recognised as a useful resource in quantum information and computation. This applies primarily to pure state entanglement which is, due to interaction with the environment, rarely available. Decoherence provides the main motivation for the study of entanglement distillation. A remarkable effect in the context of distillation is the existence of bound entangled states, states from which no pure state entanglement can be distilled. The concept of entanglement distillation also relates to a canonical way of theoretically quantifying mixed state entanglement. This thesis is, apart from a review chapter on distillation, mainly a theoretical study of bound entanglement and the two major open problems in their classification. The first of these is the classification of PPT bound entanglement (separability problem). After having reviewed known tools we study in detail the multipartite permutation criteria, for which we present new results in their classification. We solve an open problem on the existence of certain PPT states. The Schmidt number of a quantum state is a largely unvalued concept, we analyse it in detail and introduce the Schmidt robustness. The notion of Schmidt number is exploited in the study of the second
4 TENSOR COMMUTATION MATRICES AND SOME GENERALIZATIONS OF THE PAULI MATRICES
, 2014
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The classicalquantum boundary for correlations: discord and related measures
, 2012
"... One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are amongst the more activelystudied topics of quantum information theory over the ..."
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One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are amongst the more activelystudied topics of quantum information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here we review different notions of classical and quantum correlations quantified by quantum discord and other related measures. In the first half, we review the mathematical properties of the measures of quantum correlations, relate them to each other, and discuss the classicalquantum division that is common among them. In the second half, we show that the measures identify and quantify the deviation from classicality in various quantuminformationprocessing tasks, quantum thermodynamics, opensystem dynamics, and manybody physics. We show that in many cases quantum correlations indicate an advantage of quantum