4,433 research outputs found
A simple construction of complex equiangular lines
A set of vectors of equal norm in represents equiangular lines
if the magnitudes of the inner product of every pair of distinct vectors in the
set are equal. The maximum size of such a set is , and it is conjectured
that sets of this maximum size exist in for every . We
describe a new construction for maximum-sized sets of equiangular lines,
exposing a previously unrecognized connection with Hadamard matrices. The
construction produces a maximum-sized set of equiangular lines in dimensions 2,
3 and 8.Comment: 11 pages; minor revisions and comments added in section 1 describing
a link to previously known results; correction to Theorem 1 and updates to
reference
On the interpretation of lateral manganin gauge stress measurements in polymers
Encapsulated wire-element stress gauges enable changes in lateral stress during
shock loading to be directly monitored. However, there is substantial debate
with regards to interpretation of observed changes in stress behind the shock
front; a phenomenon attributed both to changes in material strength and shock-
dispersion within the gauge-encapsulation. Here, a pair of novel techniques
which both modify or remove the embedding medium where such stress gauges are
placed within target materials have been used to try and inform this debate. The
behavior of three polymeric materials of differing complexity was considered,
namely polystyrene, the commercially important resin transfer moulding RTM 6
resin and a commercially available fat lard. Comparison to the response of
embedded gauges has suggested a possible slight decrease in the absolute
magnitude of stress. However, changing the encapsulation has no detectable
effect on the gradient behind the shock in such polymeric systems
SIC~POVMs and Clifford groups in prime dimensions
We show that in prime dimensions not equal to three, each group covariant
symmetric informationally complete positive operator valued measure (SIC~POVM)
is covariant with respect to a unique Heisenberg--Weyl (HW) group. Moreover,
the symmetry group of the SIC~POVM is a subgroup of the Clifford group. Hence,
two SIC~POVMs covariant with respect to the HW group are unitarily or
antiunitarily equivalent if and only if they are on the same orbit of the
extended Clifford group. In dimension three, each group covariant SIC~POVM may
be covariant with respect to three or nine HW groups, and the symmetry group of
the SIC~POVM is a subgroup of at least one of the Clifford groups of these HW
groups respectively. There may exist two or three orbits of equivalent
SIC~POVMs for each group covariant SIC~POVM, depending on the order of its
symmetry group. We then establish a complete equivalence relation among group
covariant SIC~POVMs in dimension three, and classify inequivalent ones
according to the geometric phases associated with fiducial vectors. Finally, we
uncover additional SIC~POVMs by regrouping of the fiducial vectors from
different SIC~POVMs which may or may not be on the same orbit of the extended
Clifford group.Comment: 30 pages, 1 figure, section 4 revised and extended, published in J.
Phys. A: Math. Theor. 43, 305305 (2010
Mutually unbiased bases: tomography of spin states and star-product scheme
Mutually unbiased bases (MUBs) are considered within the framework of a
generic star-product scheme. We rederive that a full set of MUBs is adequate
for a spin tomography, i.e. knowledge of all probabilities to find a system in
each MUB-state is enough for a state reconstruction. Extending the ideas of the
tomographic-probability representation and the star-product scheme to
MUB-tomography, dequantizer and quantizer operators for MUB-symbols of spin
states and operators are introduced, ordinary and dual star-product kernels are
found. Since MUB-projectors are to obey specific rules of the star-product
scheme, we reveal the Lie algebraic structure of MUB-projectors and derive new
relations on triple- and four-products of MUB-projectors. Example of qubits is
considered in detail. MUB-tomography by means of Stern-Gerlach apparatus is
discussed.Comment: 11 pages, 1 table, partially presented at the 17th Central European
Workshop on Quantum Optics (CEWQO'2010), June 6-11, 2010, St. Andrews,
Scotland, U
Kisses of death in the graduate school application process
A survey of psychology graduate admissions committee chairs revealed 5 categories of mistakes applicants make that diminish their probability of acceptance. We discuss 3 strategies that psychology departments can use to decrease the likelihood that students will commit these mistakes in their graduate school applications and provide suggestions that will help students avoid these mistakes. The ideal student, seen through the eyes of graduate faculty, is gifted and creative, very bright and extremely motivated to learn, perfectly suited to the program, eager to actively pursue the lines of inquiry valued by the faculty, pleasant, responsible, and devoid of serious personal problems
Kisses of death in the graduate school application process
A survey of psychology graduate admissions committee chairs revealed 5 categories of mistakes applicants make that diminish their probability of acceptance. We discuss 3 strategies that psychology departments can use to decrease the likelihood that students will commit these mistakes in their graduate school applications and provide suggestions that will help students avoid these mistakes. The ideal student, seen through the eyes of graduate faculty, is gifted and creative, very bright and extremely motivated to learn, perfectly suited to the program, eager to actively pursue the lines of inquiry valued by the faculty, pleasant, responsible, and devoid of serious personal problems
From SICs and MUBs to Eddington
This is a survey of some very old knowledge about Mutually Unbiased Bases
(MUB) and Symmetric Informationally Complete POVMs (SIC). In prime dimensions
the former are closely tied to an elliptic normal curve symmetric under the
Heisenberg group, while the latter are believed to be orbits under the
Heisenberg group in all dimensions. In dimensions 3 and 4 the SICs are
understandable in terms of elliptic curves, but a general statement escapes us.
The geometry of the SICs in 3 and 4 dimensions is discussed in some detail.Comment: 12 pages; from the Festschrift for Tony Sudber
The private, the public and the hybrid in umbilical cord blood banking – a global perspective
No description supplie
Kinetic Resolution in Asymmetric Epoxidation using Iminium Salt Catalysis
The first reported examples of kinetic resolution in epoxidation reactions using iminium salt catalysis are described, providing up to 99% ee in the epoxidation of racemic cis-chromenes
Long quantum channels for high-quality entanglement transfer
High-quality quantum-state and entanglement transfer can be achieved in an
unmodulated spin bus operating in the ballistic regime, which occurs when the
endpoint qubits A and B are coupled to the chain by an exchange interaction
comparable with the intrachain exchange. Indeed, the transition amplitude
characterizing the transfer quality exhibits a maximum for a finite optimal
value , where is the channel length. We show that
scales as for large and that it ensures a
high-quality entanglement transfer even in the limit of arbitrarily long
channels, almost independently of the channel initialization. For instance, the
average quantum-state transmission fidelity exceeds 90% for any chain length.
We emphasize that, taking the reverse point of view, should be
experimentally constrained, high-quality transfer can still be obtained by
adjusting the channel length to its optimal value.Comment: 12 pages, 9 figure
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