12,106 research outputs found
Miscellaneous Applications of Quons
This paper deals with quon algebras or deformed oscillator algebras, for
which the deformation parameter is a root of unity. We show the interest of
such algebras for fractional supersymmetric quantum mechanics, angular momentum
theory and quantum information. More precisely, quon algebras are used for (i)
a realization of a generalized Weyl-Heisenberg algebra from which it is
possible to associate a fractional supersymmetric dynamical system, (ii) a
polar decomposition of SU_2 and (iii) a construction of mutually unbiased bases
in Hilbert spaces of prime dimension. We also briefly discuss (symmetric
informationally complete) positive operator valued measures in the spirit of
(iii).Comment: This is a contribution to the Proc. of the 3-rd Microconference
"Analytic and Algebraic Methods III"(June 19, 2007, Prague, Czech Republic),
published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
DEVELOPING COUNTRIES AND THE URUGUAY ROUND NEGOTIATIONS ON AGRICULTURE
International Relations/Trade,
Unitary reflection groups for quantum fault tolerance
This paper explores the representation of quantum computing in terms of
unitary reflections (unitary transformations that leave invariant a hyperplane
of a vector space). The symmetries of qubit systems are found to be supported
by Euclidean real reflections (i.e., Coxeter groups) or by specific imprimitive
reflection groups, introduced (but not named) in a recent paper [Planat M and
Jorrand Ph 2008, {\it J Phys A: Math Theor} {\bf 41}, 182001]. The
automorphisms of multiple qubit systems are found to relate to some Clifford
operations once the corresponding group of reflections is identified. For a
short list, one may point out the Coxeter systems of type and (for
single qubits), and (for two qubits), and (for three
qubits), the complex reflection groups and groups No 9 and 31 in
the Shephard-Todd list. The relevant fault tolerant subsets of the Clifford
groups (the Bell groups) are generated by the Hadamard gate, the phase
gate and an entangling (braid) gate [Kauffman L H and Lomonaco S J 2004 {\it
New J. of Phys.} {\bf 6}, 134]. Links to the topological view of quantum
computing, the lattice approach and the geometry of smooth cubic surfaces are
discussed.Comment: new version for the Journal of Computational and Theoretical
Nanoscience, focused on "Technology Trends and Theory of Nanoscale Devices
for Quantum Applications
The Protein Precursors of Peptides That Affect the Mechanics of Connective Tissue and/or Muscle in the Echinoderm Apostichopus japonicus
PMCID: PMC3432112This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
An angular momentum approach to quadratic Fourier transform, Hadamard matrices, Gauss sums, mutually unbiased bases, unitary group and Pauli group
The construction of unitary operator bases in a finite-dimensional Hilbert
space is reviewed through a nonstandard approach combinining angular momentum
theory and representation theory of SU(2). A single formula for the bases is
obtained from a polar decomposition of SU(2) and analysed in terms of cyclic
groups, quadratic Fourier transforms, Hadamard matrices and generalized Gauss
sums. Weyl pairs, generalized Pauli operators and their application to the
unitary group and the Pauli group naturally arise in this approach.Comment: Topical review (40 pages). Dedicated to the memory of Yurii
Fedorovich Smirno
The Response of Consumption to Income Shocks: Evidence from the Indian Trade Liberalization
This paper uses the Indian tariff reforms of the early nineties to estimate how households responded to the negative income shocks caused by the tariff decreases. Households more hurt by the tariff reform decreased overall expenditure, but the response is not uniform across food items. In particular, households more hurt by the reform did not change their consumption of cereals, but decreased their consumption of all other food items. Although this coping mechanism helped maintain overall levels of calorie consumption, diet diversity and the associated benefits were sacrificed.Nutrition, Trade, Development, Food Consumption/Nutrition/Food Safety, Food Security and Poverty, International Development, D7, D8, H2, O2,
Quantum Entanglement and Projective Ring Geometry
The paper explores the basic geometrical properties of the observables
characterizing two-qubit systems by employing a novel projective ring geometric
approach. After introducing the basic facts about quantum complementarity and
maximal quantum entanglement in such systems, we demonstrate that the
1515 multiplication table of the associated four-dimensional matrices
exhibits a so-far-unnoticed geometrical structure that can be regarded as three
pencils of lines in the projective plane of order two. In one of the pencils,
which we call the kernel, the observables on two lines share a base of Bell
states. In the complement of the kernel, the eight vertices/observables are
joined by twelve lines which form the edges of a cube. A substantial part of
the paper is devoted to showing that the nature of this geometry has much to do
with the structure of the projective lines defined over the rings that are the
direct product of copies of the Galois field GF(2), with = 2, 3 and 4.Comment: 13 pages, 6 figures Fig. 3 improved, typos corrected; Version 4:
Final Version Published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
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