3,447 research outputs found
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
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
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 charged beam dumps for the international linear collider
The baseline configuration of the International Linear Collider requires 2
beam dumps per interaction region, each rated to 18MW of beam power, together
with additional beam dumps for tuning purposes and machine protection. The
baseline design uses high pressure moving water dumps, first developed for the
SLC and used in the TESLA design, although a gas based dump is also being
considered. In this paper we discuss the progress made by the international
community on both physics and engineering studies for the beam dumps.Comment: Presented at European Particle Accelerator Conference (EPAC 06),
Edinburgh, Scotland, 26-30 Jun 200
On cubic difference equations with variable coefficients and fading stochastic perturbations
We consider the stochastically perturbed cubic difference equation with variable coefficients xn+1=xn(1âhnx2n)+Ïn+1Οn+1,nâN,x0âR. Here (Οn)nâN is a sequence of independent random variables, and (Ïn)nâN and (hn)nâN are sequences of nonnegative real numbers. We can stop the sequence (hn)nâN after some random time N so it becomes a constant sequence, where the common value is an FN -measurable random variable. We derive conditions on the sequences (hn)nâN , (Ïn)nâN and (Οn)nâN , which guarantee that limnââxn exists almost surely (a.s.), and that the limit is equal to zero a.s. for any initial value x0âR
The Lie Algebraic Significance of Symmetric Informationally Complete Measurements
Examples of symmetric informationally complete positive operator valued
measures (SIC-POVMs) have been constructed in every dimension less than or
equal to 67. However, it remains an open question whether they exist in all
finite dimensions. A SIC-POVM is usually thought of as a highly symmetric
structure in quantum state space. However, its elements can equally well be
regarded as a basis for the Lie algebra gl(d,C). In this paper we examine the
resulting structure constants, which are calculated from the traces of the
triple products of the SIC-POVM elements and which, it turns out, characterize
the SIC-POVM up to unitary equivalence. We show that the structure constants
have numerous remarkable properties. In particular we show that the existence
of a SIC-POVM in dimension d is equivalent to the existence of a certain
structure in the adjoint representation of gl(d,C). We hope that transforming
the problem in this way, from a question about quantum state space to a
question about Lie algebras, may help to make the existence problem tractable.Comment: 56 page
On the shock behaviour and response of Ovis Aries vertebrae
When investigating a biological system during shock loading, it is best practice to isolate different components to fully comprehend each individual part [1,2] before building up the system as a whole. Due to the high acoustic impedance of bone in comparison to other biological tissues [3] the majority of the shock will be transmitted into this medium, and as such can cause large amounts of damage to other parts of the body potentially away from the impact area
A Re-Examination of the Taxonomic Boundaries of \u3cem\u3eSymphysia\u3c/em\u3e (Ericaceae)
DNA sequence data were generated for the nuclear ITS region for Symphysia racemosa and for 26 additional Vaccinieae representing 12 sections in the genus Vaccinium plus one species from each of five additional segregate genera. Our focus is on the placement of S. racemosa relative to Vaccinium sensu scricto and Vaccinium sect. Oreades (represented by V. poasanum). Maximum parsimony analysis of 608 bp of nrITS region suggests that S. racemosa and V. poasanum form a well-supported clade in spite of substantial morphological divergence. Futhermore, this clade is a sister group to a clade consisting of all segregate genera examined. These molecular results led us to undertake a morphological cladistic analysis of all of the other Central American green-flowered taxa. We suggest that the genus Symphysia should be expanded to encompass these 15 taxa, despite the lack of phylogenetic resolution within this group. This will necessitate eight new combinations, via. Symphysia almedae (= V. almedae), Symphysia costaricensis (= V. costaricense), Symphysia jefensis (= V. jefense), Symphysia orosiensis (= V. orosiense), Symphysia ovata (= Lateropora ovata), Symphysia perardua (= V. santafeënsis), Symphysia poasana (= Vaccinium poasanum), Symphysia santafeënsis (= L. santafeënsis), and Symphysia tubulifera (= L. tubulifera)
Cancer incidence in British vegetarians
Background:
Few prospective studies have examined cancer incidence among vegetarians.
Methods:
We studied 61 566 British men and women, comprising 32 403 meat eaters, 8562 non-meat eaters who did eat fish ('fish eaters') and 20 601 vegetarians. After an average follow-up of 12.2 years, there were 3350 incident cancers of which 2204 were among meat eaters, 317 among fish eaters and 829 among vegetarians. Relative risks (RRs) were estimated by Cox regression, stratified by sex and recruitment protocol and adjusted for age, smoking, alcohol, body mass index, physical activity level and, for women only, parity and oral contraceptive use.
Results:
There was significant heterogeneity in cancer risk between groups for the following four cancer sites: stomach cancer, RRs (compared with meat eaters) of 0.29 (95% CI: 0.07â1.20) in fish eaters and 0.36 (0.16â0.78) in vegetarians, P for heterogeneity=0.007; ovarian cancer, RRs of 0.37 (0.18â0.77) in fish eaters and 0.69 (0.45â1.07) in vegetarians, P for heterogeneity=0.007; bladder cancer, RRs of 0.81 (0.36â1.81) in fish eaters and 0.47 (0.25â0.89) in vegetarians, P for heterogeneity=0.05; and cancers of the lymphatic and haematopoietic tissues, RRs of 0.85 (0.56â1.29) in fish eaters and 0.55 (0.39â0.78) in vegetarians, P for heterogeneity=0.002. The RRs for all malignant neoplasms were 0.82 (0.73â0.93) in fish eaters and 0.88 (0.81â0.96) in vegetarians (P for heterogeneity=0.001).
Conclusion:
The incidence of some cancers may be lower in fish eaters and vegetarians than in meat eaters
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