918,240 research outputs found
Operator-Schmidt decomposition of the quantum Fourier transform on C^N1 tensor C^N2
Operator-Schmidt decompositions of the quantum Fourier transform on C^N1
tensor C^N2 are computed for all N1, N2 > 1. The decomposition is shown to be
completely degenerate when N1 is a factor of N2 and when N1>N2. The first known
special case, N1=N2=2^n, was computed by Nielsen in his study of the
communication cost of computing the quantum Fourier transform of a collection
of qubits equally distributed between two parties. [M. A. Nielsen, PhD Thesis,
University of New Mexico (1998), Chapter 6, arXiv:quant-ph/0011036.] More
generally, the special case N1=2^n1<2^n2=N2 was computed by Nielsen et. al. in
their study of strength measures of quantum operations. [M.A. Nielsen et. al,
(accepted for publication in Phys Rev A); arXiv:quant-ph/0208077.] Given the
Schmidt decompositions presented here, it follows that in all cases the
communication cost of exact computation of the quantum Fourier transform is
maximal.Comment: 9 pages, LaTeX 2e; No changes in results. References and
acknowledgments added. Changes in presentation added to satisfy referees:
expanded introduction, inclusion of ommitted algebraic steps in the appendix,
addition of clarifying footnote
On the description of Leibniz superalgebras of nilindex n+m
In this work we investigate the complex Leibniz superalgebras with
characteristic sequence (n1, . . . , nk|m) and nilindex n + m, where n = n1 +
· · ·+nk, n and m (m 6= 0) are dimensions of even and odd parts, respectively.
Such superalgebras with condition n1 ≥ n − 1 were classified in [4]–[5]. Here
we prove that in the case n1 ≤ n − 2 the Leibniz superalgebras have nilindex
less than n +m. Thus, we get the classification of Leibniz superalgebras with
characteristic sequence (n1, . . . , nk|m) and nilindex n +m
Generating all permutations by context-free grammars in Chomsky normal form
Let Ln be the finite language of all n! strings that are permutations of n different symbols (n1). We consider context-free grammars Gn in Chomsky normal form that generate Ln. In particular we study a few families {Gn}n1, satisfying L(Gn)=Ln for n1, with respect to their descriptional complexity, i.e. we determine the number of nonterminal symbols and the number of production rules of Gn as functions of n
Rarita-Schwinger-Weyl semimetal in Jeff=3/2 electron systems
We propose a relativistic Jeff=3/2 semimetal with 4d1 or 5d1 electrons on a
cubic lattice when the strong spin-orbital coupling takes over the Hunds'
coupling. A relativistic spinor with spin 3/2 is historically called
Rarita-Schwinger spinor. In the massless case, the right- and left-handed
chiral degrees of freedom of the Rarita-Schwinger spinors are independent. In
the lattice model that we propose, the right- and left- handed gapless points
in Brillouin zone are separated. We call this linearly dispersed semimetal
Rarita-Schwinger-Weyl semimetal, similar to Weyl semimetal for spin 1/2
systems. There is a network of gapless Fermi arcs in the surface Brillouin zone
if n1+n2+n3 is even for the normal vector (n1,n2,n3) of the surface while the
surface is insulator if n1+n2+n3 is odd.Comment: 5 pages, 4 figure
Quadratic Dynamical Decoupling with Non-Uniform Error Suppression
We analyze numerically the performance of the near-optimal quadratic
dynamical decoupling (QDD) single-qubit decoherence errors suppression method
[J. West et al., Phys. Rev. Lett. 104, 130501 (2010)]. The QDD sequence is
formed by nesting two optimal Uhrig dynamical decoupling sequences for two
orthogonal axes, comprising N1 and N2 pulses, respectively. Varying these
numbers, we study the decoherence suppression properties of QDD directly by
isolating the errors associated with each system basis operator present in the
system-bath interaction Hamiltonian. Each individual error scales with the
lowest order of the Dyson series, therefore immediately yielding the order of
decoherence suppression. We show that the error suppression properties of QDD
are dependent upon the parities of N1 and N2, and near-optimal performance is
achieved for general single-qubit interactions when N1=N2.Comment: 17 pages, 22 figure
Frequency Estimation Of The First Pinna Notch In Head-Related Transfer Functions With A Linear Anthropometric Model
The relation between anthropometric parameters and Head-Related Transfer Function (HRTF) features, especially those due to the pinna, are not fully understood yet. In this paper we apply signal processing techniques to extract the frequencies of the main pinna notches (known as N1, N2, and N3) in the frontal part of the median plane and build a model relating them to 13 different anthropometric parameters of the pinna, some of which depend on the elevation angle of the sound source. Results show that while the considered anthropometric parameters are not able to approximate
with sufficient accuracy neither the N2 nor the N3 frequency, eight of them are sufficient for modeling the frequency of N1 within a psychoacoustically acceptable margin of error. In particular, distances between the ear canal and the outer helix border are the most important parameters for predicting N1
Orthogonal Linear Combinations of Gaussian Type Orbitals
The set of Gaussian Type Orbitals g(n1,n2,n3) of order (n+1)(n+2)/2, of
common n=n1+n2+n3<=7, common center and exponential, is customized to define a
set of 2n+1 linear combinations t(n,m) (-n<=m<=n) such that each t(n,m) depends
on the azimuthal and polar angle of the spherical coordinate system like the
real or imaginary part of the associated Spherical Harmonic. (Results cover
both Hermite and Cartesian Gaussian Type Orbitals.) Overlap, kinetic energy and
Coulomb energy matrix elements are presented for generalized basis functions of
the type r^s*t(n,m) (s=0,2,4,...). In addition, normalization integrals int
|g(n1,n2,n3)|d^3r are calculated up to n=7 and normalization integrals int
|r^s*t(n,m)|d^3r up to n=5.Comment: 13 pages, no figures, REVTeX4. Corrected eqs. (23) and (C4
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