109,996 research outputs found
Group theoretic, Lie algebraic and Jordan algebraic formulations of the SIC existence problem
Although symmetric informationally complete positive operator valued measures
(SIC POVMs, or SICs for short) have been constructed in every dimension up to
67, a general existence proof remains elusive. The purpose of this paper is to
show that the SIC existence problem is equivalent to three other, on the face
of it quite different problems. Although it is still not clear whether these
reformulations of the problem will make it more tractable, we believe that the
fact that SICs have these connections to other areas of mathematics is of some
intrinsic interest. Specifically, we reformulate the SIC problem in terms of
(1) Lie groups, (2) Lie algebras and (3) Jordan algebras (the second result
being a greatly strengthened version of one previously obtained by Appleby,
Flammia and Fuchs). The connection between these three reformulations is
non-trivial: It is not easy to demonstrate their equivalence directly, without
appealing to their common equivalence to SIC existence. In the course of our
analysis we obtain a number of other results which may be of some independent
interest.Comment: 36 pages, to appear in Quantum Inf. Compu
The Fractional Quantum Hall States at and and their Non-Abelian Nature
We investigate the nature of the fractional quantum Hall (FQH) state at
filling factor , and its particle-hole conjugate state at ,
with the Coulomb interaction, and address the issue of possible competing
states. Based on a large-scale density-matrix renormalization group (DMRG)
calculation in spherical geometry, we present evidence that the physics of the
Coulomb ground state (GS) at and is captured by the
parafermion Read-Rezayi RR state, . We first establish that the
state at is an incompressible FQH state, with a GS protected by a
finite excitation gap, with the shift in accordance with the RR state. Then, by
performing a finite-size scaling analysis of the GS energies for
with different shifts, we find that the state has the lowest
energy among different competing states in the thermodynamic limit. We find the
fingerprint of topological order in the FQH and
states, based on their entanglement spectrum and topological entanglement
entropy, both of which strongly support their identification with the
state. Furthermore, by considering the shift-free
infinite-cylinder geometry, we expose two topologically-distinct GS sectors,
one identity sector and a second one matching the non-Abelian sector of the
Fibonacci anyonic quasiparticle, which serves as additional evidence for the
state at and .Comment: 12 pages, 8 figure
Topological Characterization of Non-Abelian Moore-Read State using Density-Matrix Renormailzation Group
The non-Abelian topological order has attracted a lot of attention for its
fundamental importance and exciting prospect of topological quantum
computation. However, explicit demonstration or identification of the
non-Abelian states and the associated statistics in a microscopic model is very
challenging. Here, based on density-matrix renormalization group calculation,
we provide a complete characterization of the universal properties of bosonic
Moore-Read state on Haldane honeycomb lattice model at filling number
for larger systems, including both the edge spectrum and the bulk anyonic
quasiparticle (QP) statistics. We first demonstrate that there are three
degenerating ground states, for each of which there is a definite anyonic flux
threading through the cylinder. We identify the nontrivial countings for the
entanglement spectrum in accordance with the corresponding conformal field
theory. Through inserting the charge flux, it is found that two of the
ground states can be adiabatically connected through a fermionic
charge- QP being pumped from one edge to the other, while the
ground state in Ising anyon sector evolves back to itself. Furthermore, we
calculate the modular matrices and , which contain
all the information for the anyonic QPs. In particular, the extracted quantum
dimensions, fusion rule and topological spins from modular matrices positively
identify the emergence of non-Abelian statistics following the
Chern-Simons theory.Comment: 5 pages; 3 figure
An investigation of pulsar searching techniques with the Fast Folding Algorithm
Here we present an in-depth study of the behaviour of the Fast Folding
Algorithm, an alternative pulsar searching technique to the Fast Fourier
Transform. Weaknesses in the Fast Fourier Transform, including a susceptibility
to red noise, leave it insensitive to pulsars with long rotational periods (P >
1 s). This sensitivity gap has the potential to bias our understanding of the
period distribution of the pulsar population. The Fast Folding Algorithm, a
time-domain based pulsar searching technique, has the potential to overcome
some of these biases. Modern distributed-computing frameworks now allow for the
application of this algorithm to all-sky blind pulsar surveys for the first
time. However, many aspects of the behaviour of this search technique remain
poorly understood, including its responsiveness to variations in pulse shape
and the presence of red noise. Using a custom CPU-based implementation of the
Fast Folding Algorithm, ffancy, we have conducted an in-depth study into the
behaviour of the Fast Folding Algorithm in both an ideal, white noise regime as
well as a trial on observational data from the HTRU-S Low Latitude pulsar
survey, including a comparison to the behaviour of the Fast Fourier Transform.
We are able to both confirm and expand upon earlier studies that demonstrate
the ability of the Fast Folding Algorithm to outperform the Fast Fourier
Transform under ideal white noise conditions, and demonstrate a significant
improvement in sensitivity to long-period pulsars in real observational data
through the use of the Fast Folding Algorithm.Comment: 19 pages, 15 figures, 3 table
Implementation of universal quantum gates based on nonadiabatic geometric phases
We propose an experimentally feasible scheme to achieve quantum computation
based on nonadiabatic geometric phase shifts, in which a cyclic geometric phase
is used to realize a set of universal quantum gates. Physical implementation of
this set of gates is designed for Josephson junctions and for NMR systems.
Interestingly, we find that the nonadiabatic phase shift may be independent of
the operation time under appropriate controllable conditions. A remarkable
feature of the present nonadiabatic geometric gates is that there is no
intrinsic limitation on the operation time, unlike adiabatic geometric gates.
Besides fundamental interest, our results may simplify the implementation of
geometric quantum computation based on solid state systems, where the
decoherence time may be very short.Comment: 5 pages, 2 figures; the version published in Phys. Rev. Let
Quasi-reversible Magnetoresistance in Exchange Spring Tunnel Junctions
We report a large, quasi-reversible tunnel magnetoresistance in
exchange-biased ferromagnetic semiconductor tunnel junctions wherein a soft
ferromagnetic semiconductor (\gma) is exchange coupled to a hard ferromagnetic
metal (MnAs). Our observations are consistent with the formation of a region of
inhomogeneous magnetization (an "exchange spring") within the biased \gma
layer. The distinctive tunneling anisotropic magnetoresistance of \gma produces
a pronounced sensitivity of the magnetoresistance to the state of the exchange
spring
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