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

Lateral stress evolution in chromium sulfide cermets with varying excess chromium

The shock response of chromium sulfide-chromium, a cermet of potential interest as a matrix material for ballistic applications, has been investigated at two molar ratios. Using a combustion synthesis technique allowed for control of the molar ratio of the material, which was investigated under near-stoichiometric (cermet) and excess chromium (interpenetrating composite) conditions, representing chromium:sulfur molar ratios of 1.15:1 and 4:1, respectively. The compacts were investigated via the plate-impact technique, which allowed the material to be loaded under a onedimensional state of strain. Embedded manganin stress gauges were employed to monitor the temporal evolution of longitudinal and lateral components of stress in both materials. Comparison of these two components has allowed assessment of the variation of material shear strength both with impact pressure/strain-rate and time for the two molar ratio conditions. The two materials exhibited identical material strength despite variations in their excess chromium content

Pelletizing

DURING the last 15 or 20 years we have witnessed an extra-ordinary increase in the quantity of artificial agglomera-tes used in blast-furnace burdens. This expansion has occurred in two fields, the first being sintering, a technique applied particularly to the agglomeration of low grade 'earthy' ores and to screenings from high quality Jump

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: 0.07–1.20) in fish eaters and 0.36 (0.16–0.78) in vegetarians, P for heterogeneity=0.007; ovarian cancer, RRs of 0.37 (0.18–0.77) in fish eaters and 0.69 (0.45–1.07) in vegetarians, P for heterogeneity=0.007; bladder cancer, RRs of 0.81 (0.36–1.81) in fish eaters and 0.47 (0.25–0.89) in vegetarians, P for heterogeneity=0.05; and cancers of the lymphatic and haematopoietic tissues, RRs of 0.85 (0.56–1.29) in fish eaters and 0.55 (0.39–0.78) in vegetarians, P for heterogeneity=0.002. The RRs for all malignant neoplasms were 0.82 (0.73–0.93) in fish eaters and 0.88 (0.81–0.96) 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

Control of quantum interference in the quantum eraser

We have implemented an optical quantum eraser with the aim of studying this phenomenon in the context of state discrimination. An interfering single photon is entangled with another one serving as a which-path marker. As a consequence, the visibility of the interference as well as the which-path information are constrained by the overlap (measured by the inner product) between the which-path marker states, which in a more general situation are non-orthogonal. In order to perform which-path or quantum eraser measurements while analyzing non-orthogonal states, we resort to a probabilistic method for the unambiguous modification of the inner product between the two states of the which-path marker in a discrimination-like process.Comment: Submitted to New Journal of Physics, March 200

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

Generalized Brans-Dicke theories

In Brans-Dicke theory a non-linear self interaction of a scalar field allows a possibility of realizing the late-time cosmic acceleration, while recovering the General Relativistic behavior at early cosmological epochs. We extend this to more general modified gravitational theories in which a de Sitter solution for dark energy exists without using a field potential. We derive a condition for the stability of the de Sitter point and study the background cosmological dynamics of such theories. We also restrict the allowed region of model parameters from the demand for the avoidance of ghosts and instabilities. A peculiar evolution of the field propagation speed allows us to distinguish those theories from the LCDM model.Comment: 14 pages, 4 figures, version to appear in JCA

TDP43 proteinopathy is associated with aberrant DNA methylation in human amyotrophic lateral sclerosis

Background Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disease characterized by motor neurone (MN) degeneration and death. ALS can be sporadic (sALS) or familial, with a number of associated gene mutations, including C9orf72 (C9ALS). DNA methylation is an epigenetic mechanism whereby a methyl group is attached to a cytosine (5mC), resulting in gene expression repression. 5mC can be further oxidized to 5‐hydroxymethylcytosine (5hmC). DNA methylation has been studied in other neurodegenerative diseases, but little work has been conducted in ALS. Aims To assess differences in DNA methylation in individuals with ALS and the relationship between DNA methylation and TDP43 pathology. Methods Post mortem tissue from controls, sALS cases and C9ALS cases were assessed by immunohistochemistry for 5mC and 5hmC in spinal cord, motor cortex and prefrontal cortex. LMNs were extracted from a subset of cases using laser capture microdissection. DNA from these underwent analysis using the MethylationEPIC array to determine which molecular processes were most affected. Results There were higher levels of 5mC and 5hmC in sALS and C9ALS in the residual lower motor neurones (LMNs) of the spinal cord. Importantly, in LMNs with TDP43 pathology there was less nuclear 5mC and 5hmC compared to the majority of residual LMNs that lacked TDP43 pathology. Enrichment analysis of the array data suggested RNA metabolism was particularly affected. Conclusions DNA methylation is a contributory factor in ALS LMN pathology. This is not so for glia or neocortical neurones