405 research outputs found
Superdense Coding with GHZ and Quantum Key Distribution with W in the ZX-calculus
No full textQuantum entanglement is a key resource in many quantum protocols, such as quantum teleportation and quantum cryptography. Yet entanglement makes protocols presented in Dirac notation difficult to verify. This is why Coecke and Duncan have introduced a diagrammatic language for quantum protocols, called the ZX-calculus. This diagrammatic notation is both intuitive and formally rigorous. It is a simple, graphical, high level language that emphasises the composition of systems and naturally captures the essentials of quantum mechanics. In the author's MSc thesis it has been shown for over 25 quantum protocols that the ZX-calculus provides a relatively easy and more intuitive presentation. Moreover, the author embarked on the task to apply categorical quantum mechanics on quantum security; earlier works did not touch anything but Bennett and Brassard's quantum key distribution protocol, BB84. Superdense coding with the Greenberger-Horne-Zeilinger state and quantum key distribution with the W-state are presented in the ZX-calculus in this paper
On-top pair-correlation function in the homogeneous electron liquid
No full textThe ladder theory, in which the Bethe-Goldstone equation for the effective potential between two scattering particles plays a central role, is well known for its satisfactory description of the short-range correlations in the homogeneous electron liquid. By solving exactly the Bethe-Goldstone equation in the limit of large transfer momentum between two scattering particles, we obtain accurate results for the on-top pair-correlation function g(0), in both three dimensions and two dimensions. Furthermore, we prove, in general, that the ladder theory satisfies the cusp condition for the pair-correlation function g(r) at zero distance r=0.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000235009500047&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701Physics, Condensed MatterSCI(E)8ARTICLE3null7
Improved fifth-order geometric aberration coeincients of electron lenses
No full textIn this paper, fifth-order geometric aberrations of round electron lenses have been restudied. Improved analytical formulae of the aberration coefficients were derived by the computer algebra software-Mathematica-and their correctness verified by cross-checking with numerical integration and differential algebraic techniques for a given electromagnetic lens.Physics, AppliedSCI(E)EI3ARTICLE5653-6593
Long-wavelength behavior of the dynamical spin-resolved local-field factor in a two-dimensional electron liquid
No full textThe high-frequency limits of the singular component A(omega) of the small wave-vector expansion of the longitudinal (L) and transverse (T) components of the spin-resolved exchange-correlation kernel tensor f(xc,sigmasigma)('L,T)(q,omega)=-v(q)G(sigmasigma)('L,T)(q,omega) in a two-dimensional isotropic electron liquid with arbitrary spin polarization are studied. Here G(sigmasigma)('L,T)(q,omega) is the spin-resolved local-field factor, v(q) is the Coulomb interaction in momentum space, and sigma denotes spin. Particularly, the real part of A(omega) is found to be logarithmically divergent at large omega. The large wave-vector structure of the corresponding spin-resolved static structure factor is also established.Physics, Condensed MatterSCI(E)1ARTICLE23null7
ZX-Calculs pour l'Informatique Quantique et leur Complétude
No full textThe ZX-Calculus is a powerful and intuitive graphical language, based on category theory, that allows for quantum reasoning and computing. Quantum evolutions are seen in this formalism as open graphs, or diagrams, that can be transformed locally according to a set of axioms that preserve the result of the computation. One of the most important aspects of language is its completeness: Given two diagrams that represent the same quantum evolution, can I transform one into the other using only the graphical rules allowed by the language? If this is the case, it means that the graphical language captures quantum mechanics entirely.The language is known to be complete for a particular subclass (or fragment) of quantum evolutions, called Clifford. Unfortunately, this one is not universal: we cannot represent, or even approach, certain quantum evolutions. In this thesis, we propose to extend the set of axioms to obtain completeness for larger fragments of the language, which in particular are approximately universal, or even universal.To do this, we first use the completeness of another graphical language and transport this result to the ZX-Calculus. In order to simplify this tedious step, we introduce an intermediate language, interesting in itself as it captures a particular but universal fragment of quantum mechanics: Toffoli-Hadamard.We then define the notion of a linear diagram, which provides a uniform proof for some sets of equations.We also define the notion of singular value decomposition of a diagram, which allows us to avoid a largenumber of calculations.In a second step, we define a normal form that exists for an infinite number of fragments of the language, as well as for the language itself, without restriction. Thanks to this, we reprove the previous completeness results, but this time without using any third party language, and we derive new ones for other fragments. The controlled states, used for the definition of the normal form, are also useful for performing non-trivial operations such as sum, term-to-term product, or concatenation.Le ZX-Calculus est un langage graphique puissant et intuitif, issu de la théorie des catégories, et qui permet de raisonner et calculer en quantique. Les évolutions quantiques sont vues dans ce formalisme comme des graphes ouverts, ou diagrammes, qui peuvent être transformés localement selon un ensemble d’axiomes qui preservent le résultat du calcul. Un aspect des plus importants du langage est sa complétude : Étant donnés deux diagrammes qui représentent la même évolution quantique, puis-je transformer l’un en l’autre en utilisant seulement les règles graphiques permises par le langage ? Si c’est le cas, cela veut dire que le langage graphique capture entièrement la mécanique quantique.Le langage est connu comme étant complet pour une sous-classe (ou fragment) particulière d’évolutions quantiques, appelée Clifford. Malheureusement, celle-ci n’est pas universelle : on ne peut pas représenter, ni même approcher, certaines évolutions. Dans cette thèse, nous proposons d’élargir l’ensemble d’axiomes pour obtenir la complétude pour des fragments plus grands du langage, qui en particuliersont approximativement universels, voire universels.Pour ce faire, dans un premier temps nous utilisons la complétude d’un autre langage graphique et transportons ce résultat au ZX-Calculus. Afin de simplifier cette fastidieuse étape, nous introduisons un langage intermédiaire, intéressant en lui-même car il capture un fragment particulier mais universel de la mécanique quantique : Toffoli-Hadamard. Nous définissons ensuite la notion de diagramme linéaire, qui permet d’obtenir une preuve uniforme pour certains ensembles d’équations. Nous définissons également la notion de décomposition d’un diagramme en valeurs singuliaires, ce qui nous permet de nous épargner un grand nombre de calculs.Dans un second temps, nous définissons une forme normale qui a le mérite d’exister pour une infinité de fragments du langage, ainsi que pour le langage lui-même, sans restriction. Grâce à cela, nous reprouvons les résultats de complétude précédents, mais cette fois sans utiliser de langage tiers, et nous en dérivons de nouveaux, pour d’autres fragments. Les états contrôlés, utilisés pour la définition de forme normale, s’avèrent en outre utiles pour réaliser des opérations non-triviales telles que la somme, le produit terme-à-terme, ou la concaténation
ZX-Calculs pour l'Informatique Quantique et leur Complétude
No full textThe ZX-Calculus is a powerful and intuitive graphical language, based on category theory, that allows for quantum reasoning and computing. Quantum evolutions are seen in this formalism as open graphs, or diagrams, that can be transformed locally according to a set of axioms that preserve the result of the computation. One of the most important aspects of language is its completeness: Given two diagrams that represent the same quantum evolution, can I transform one into the other using only the graphical rules allowed by the language? If this is the case, it means that the graphical language captures quantum mechanics entirely.The language is known to be complete for a particular subclass (or fragment) of quantum evolutions, called Clifford. Unfortunately, this one is not universal: we cannot represent, or even approach, certain quantum evolutions. In this thesis, we propose to extend the set of axioms to obtain completeness for larger fragments of the language, which in particular are approximately universal, or even universal.To do this, we first use the completeness of another graphical language and transport this result to the ZX-Calculus. In order to simplify this tedious step, we introduce an intermediate language, interesting in itself as it captures a particular but universal fragment of quantum mechanics: Toffoli-Hadamard.We then define the notion of a linear diagram, which provides a uniform proof for some sets of equations.We also define the notion of singular value decomposition of a diagram, which allows us to avoid a largenumber of calculations.In a second step, we define a normal form that exists for an infinite number of fragments of the language, as well as for the language itself, without restriction. Thanks to this, we reprove the previous completeness results, but this time without using any third party language, and we derive new ones for other fragments. The controlled states, used for the definition of the normal form, are also useful for performing non-trivial operations such as sum, term-to-term product, or concatenation.Le ZX-Calculus est un langage graphique puissant et intuitif, issu de la théorie des catégories, et qui permet de raisonner et calculer en quantique. Les évolutions quantiques sont vues dans ce formalisme comme des graphes ouverts, ou diagrammes, qui peuvent être transformés localement selon un ensemble d’axiomes qui preservent le résultat du calcul. Un aspect des plus importants du langage est sa complétude : Étant donnés deux diagrammes qui représentent la même évolution quantique, puis-je transformer l’un en l’autre en utilisant seulement les règles graphiques permises par le langage ? Si c’est le cas, cela veut dire que le langage graphique capture entièrement la mécanique quantique.Le langage est connu comme étant complet pour une sous-classe (ou fragment) particulière d’évolutions quantiques, appelée Clifford. Malheureusement, celle-ci n’est pas universelle : on ne peut pas représenter, ni même approcher, certaines évolutions. Dans cette thèse, nous proposons d’élargir l’ensemble d’axiomes pour obtenir la complétude pour des fragments plus grands du langage, qui en particuliersont approximativement universels, voire universels.Pour ce faire, dans un premier temps nous utilisons la complétude d’un autre langage graphique et transportons ce résultat au ZX-Calculus. Afin de simplifier cette fastidieuse étape, nous introduisons un langage intermédiaire, intéressant en lui-même car il capture un fragment particulier mais universel de la mécanique quantique : Toffoli-Hadamard. Nous définissons ensuite la notion de diagramme linéaire, qui permet d’obtenir une preuve uniforme pour certains ensembles d’équations. Nous définissons également la notion de décomposition d’un diagramme en valeurs singuliaires, ce qui nous permet de nous épargner un grand nombre de calculs.Dans un second temps, nous définissons une forme normale qui a le mérite d’exister pour une infinité de fragments du langage, ainsi que pour le langage lui-même, sans restriction. Grâce à cela, nous reprouvons les résultats de complétude précédents, mais cette fois sans utiliser de langage tiers, et nous en dérivons de nouveaux, pour d’autres fragments. Les états contrôlés, utilisés pour la définition de forme normale, s’avèrent en outre utiles pour réaliser des opérations non-triviales telles que la somme, le produit terme-à-terme, ou la concaténation
APFIM AND FEM STUDY OF MO-LA ALLOY WIRE
No full textPhysics, MultidisciplinarySCI(E)0ARTICLEC-6283-2864
A STUDY OF MINIATURIZED ELECTROSTATIC OCTUPOLE DEFLECTORS
No full textIn this paper the computer simulation and the computational results of miniaturized electrostatic octupole deflectors have been presented. It has been shown that both axial and azimuthal fringing effects must be taken into account for such deflectors with small length-to-radius ratio. The axial fringing effects make deflection sensitivity higher, have no effects on deflection coma and chromatism coefficients, and change the behaviors of deflection field curvature, astigmatism, and distortion coefficients for the round-lens-type aberrations. The azimuthal fringing effects decrease deflection sensitivity but hardly affect any round-lens-type deflection aberration coefficients. For miniaturized electrostatic octupole deflectors the computational results also show that four-fold deflection coma, astigmatism, and distortion are all extremly small and can be completely neglected.Instruments & InstrumentationNuclear Science & TechnologyPhysics, Particles & FieldsSpectroscopySCI(E)
Meeting the Kyoto targets: the importance of developing country participation
No full textThis paper investigates the implications of progressively broadening the scope of the market of tradable permits from no emissions trading to full global trading. We start with the no emissions trading case where each Annex I country must individually meet its Kyoto targets. Next, we consider a case where trading of emissions permits is limited to Annex I countries only. We then expand the scope of the market to include all the non-Annex I countries but China. Finally, to investigate the role China plays in bringing down Annex I countries' compliance costs, we further broaden the market to include China into full global trading. Our results clearly demonstrate that the gain of the OECD as a whole increases as the market expands. Our results also show that developing countries themselves benefit from such an expansion too because it not only provides them for additional financial resources, but also helps to cut their baseline carbon emissions by a big margin. By contrast, the former Soviet Union tends to become worse off as the market expands. The potential conflict of interest between the former Soviet Union and developing countries underlines the importance of establishing clear rules of procedure about admitting new entrants before emissions trading begins. Furthermore, our results show that China is expected to emerge as the world's number one host country for clean development mechanism projects, but to materialise such benefits, China faces great challenges in institutional setting and implementation strategy. (C) 2004 Society for Policy Modeling. Published by Elsevier Inc. All rights reserved.EconomicsCPCI-SSH(ISSHP)SSCI2
On the nature of the lightest scalar resonances
No full textWe briefly review the recent progresses in the new unitarization approach being developed by us. Especially we discuss the large N-c pi pi scatterings by making use of the partial wave S matrix parametrization form. We find that the a pole may move to the negative real axis on the second sheet of the complex s plane, therefore it raises the interesting question that this 'sigma' pole may be related to the sigma in the linear sigma model.Physics, NuclearCPCI-S(ISTP)
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