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Quantum entanglement
, 2007
"... Contents All our former experience with application of quantum theory seems to say: what is predicted by quantum formalism must occur in laboratory. But the essence of quantum formalism — entanglement, recognized by Einstein, Podolsky, Rosen and Schrödinger — waited over 70 years to enter to laborat ..."
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Cited by 84 (1 self)
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Contents All our former experience with application of quantum theory seems to say: what is predicted by quantum formalism must occur in laboratory. But the essence of quantum formalism — entanglement, recognized by Einstein, Podolsky, Rosen and Schrödinger — waited over 70 years to enter to laboratories as a new resource as real as energy.
On Duality between Quantum Maps and Quantum States
, 2004
"... We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations, determined by unitary matrices of extended dimensionality, is ..."
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Cited by 26 (0 self)
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We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations, determined by unitary matrices of extended dimensionality, is defined and analyzed. Using the concept of the dynamical matrix and the Jamiolkowski isomorphism we explore the relation between the set of quantum operations (dynamics) and the set of density matrices acting on an extended Hilbert space (kinematics). An analogous relation is established between the classical maps and an extended space of the discrete probability distributions.
A Rosetta stone for quantum mechanics with an introduction to quantum computation
, 2002
"... Abstract. The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading ..."
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Cited by 24 (10 self)
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Abstract. The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading
Quantum hidden subgroup algorithms on free groups, (in preparation
"... Abstract. One of the most promising and versatile approaches to creating new quantum algorithms is based on the quantum hidden subgroup (QHS) paradigm, originally suggested by Alexei Kitaev. This class of quantum algorithms encompasses the DeutschJozsa, Simon, Shor algorithms, and many more. In thi ..."
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Cited by 10 (2 self)
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Abstract. One of the most promising and versatile approaches to creating new quantum algorithms is based on the quantum hidden subgroup (QHS) paradigm, originally suggested by Alexei Kitaev. This class of quantum algorithms encompasses the DeutschJozsa, Simon, Shor algorithms, and many more. In this paper, our strategy for finding new quantum algorithms is to decompose Shor’s quantum factoring algorithm into its basic primitives, then to generalize these primitives, and finally to show how to reassemble them into new QHS algorithms. Taking an ”alphabetic building blocks approach, ” we use these primitives to form an ”algorithmic toolkit ” for the creation of new quantum algorithms, such as wandering Shor algorithms, continuous Shor algorithms, the quantum circle algorithm, the dual Shor algorithm, a QHS algorithm for Feynman integrals, free QHS algorithms, and more. Toward the end of this paper, we show how Grover’s algorithm is most surprisingly “almost ” a QHS algorithm, and how this result suggests the possibility of an even more complete ”algorithmic tookit ” beyond the QHS algorithms. Contents
Quantum Programming Languages: An Introductory Overview
, 2006
"... The present article gives an introductory overview of the novel field of quantum programming languages (QPLs) from a pragmatic perspective. First, after a short summary of basic notations of quantum mechanics, some of the goals and design issues are surveyed, which motivate the research in this area ..."
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Cited by 5 (0 self)
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The present article gives an introductory overview of the novel field of quantum programming languages (QPLs) from a pragmatic perspective. First, after a short summary of basic notations of quantum mechanics, some of the goals and design issues are surveyed, which motivate the research in this area. Then, several of the approaches are described in more detail. The article concludes with a brief survey of current research activities and a tabular summary of a selection of QPLs, which have been published so far.
Quantum Information from GravitonMatter Gas ⋆
"... Abstract. We present basics of conceptually newtype way for explaining of the origin, evolution and current physical properties of our Universe from the gravitonmatter gas viewpoint. Quantization method for the Friedmann–Lemaître Universe based on the canonical Hamilton equations of motion is prop ..."
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Abstract. We present basics of conceptually newtype way for explaining of the origin, evolution and current physical properties of our Universe from the gravitonmatter gas viewpoint. Quantization method for the Friedmann–Lemaître Universe based on the canonical Hamilton equations of motion is proposed and quantum information theory way to physics of the Universe is showed. The current contribution from the gravitonmatter gas temperature in quintessence approximation is discussed.
Quantum Cat’s Dilemma: an example of intransitivity in a quantum game
 Phys.Lett.A
"... We study a quantum version of the sequential game illustrating problems connected with making rational decisions. We compare the results that the two models (quantum and classical) yield. In the quantum model intransitivity gains importance significantly. We argue that the quantum model describes ou ..."
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We study a quantum version of the sequential game illustrating problems connected with making rational decisions. We compare the results that the two models (quantum and classical) yield. In the quantum model intransitivity gains importance significantly. We argue that the quantum model describes our spontaneously shown preferences more precisely than the classical model, as these preferences are often intransitive.
Combinatorial laplacians and positivity under partial transpose
 Math. Struct. in Comp. Sci
"... Density matrices of graphs are combinatorial laplacians normalized to have trace one (Braunstein et al. Phys. Rev. A, 73:1, 012320 (2006)). If the vertices of a graph are arranged as an array, then its density matrix carries a block structure with respect to which properties such as separability can ..."
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Cited by 4 (3 self)
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Density matrices of graphs are combinatorial laplacians normalized to have trace one (Braunstein et al. Phys. Rev. A, 73:1, 012320 (2006)). If the vertices of a graph are arranged as an array, then its density matrix carries a block structure with respect to which properties such as separability can be considered. We prove that the socalled degreecriterion, which was conjectured to be necessary and sufficient for separability of density matrices of graphs, is equivalent to the PPTcriterion. Additionally, we give an alternative proof of the sufficiency of the degreecriterion when one of the array dimensions has length
Covariant Mappings for the Description of Measurement, Dissipation and Decoherence in Quantum Mechanics
, 707
"... Summary. The general formalism of quantum mechanics for the description of statistical experiments is briefly reviewed, introducing in particular position and momentum observables as POVM characterized by their covariance properties with respect to the isochronous Galilei group. Mappings describing ..."
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Summary. The general formalism of quantum mechanics for the description of statistical experiments is briefly reviewed, introducing in particular position and momentum observables as POVM characterized by their covariance properties with respect to the isochronous Galilei group. Mappings describing state transformations both as a consequence of measurement and of dynamical evolution for a closed or open system are considered with respect to the general constraints they have to obey and their covariance properties with respect to symmetry groups. In particular different master equations are analyzed in view of the related symmetry group, recalling the general structure of mappings covariant under the same group. This is done for damped harmonic oscillator, twolevel system and quantum Brownian motion. Special attention is devoted to the general structure of translationcovariant master equations. Within this framework a recently obtained quantum counterpart of the classical linear Boltzmann equation is considered, as well as a general theoretical framework for the description of different decoherence experiments, pointing to a connection between different possible behaviours in the description of decoherence and the characteristic functions of classical Lévy processes. 1