On SIC-POVMs in Prime Dimensions

The generalized Pauli group and its normalizer, the Clifford group, have a rich mathematical structure which is relevant to the problem of constructing symmetric informationally complete POVMs (SIC-POVMs). To date, almost every known SIC-POVM fiducial vector is an eigenstate of a "canonical" unitary in the Clifford group. I show that every canonical unitary in prime dimensions p > 3 lies in the same conjugacy class of the Clifford group and give a class representative for all such dimensions. It follows that if even one such SIC-POVM fiducial vector is an eigenvector of such a unitary, then all of them are (for a given such dimension). I also conjecture that in all dimensions d, the number of conjugacy classes is bounded above by 3 and depends only on d mod 9, and I support this claim with computer computations in all dimensions < 48.Comment: 6 pages, no figures. v3 Refs added, improved discussion of previous work. Ref to a proof of the main conjecture also adde

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

Salmonella Typhimurium Type III Secretion Effectors Stimulate Innate Immune Responses in Cultured Epithelial Cells

Recognition of conserved bacterial products by innate immune receptors leads to inflammatory responses that control pathogen spread but that can also result in pathology. Intestinal epithelial cells are exposed to bacterial products and therefore must prevent signaling through innate immune receptors to avoid pathology. However, enteric pathogens are able to stimulate intestinal inflammation. We show here that the enteric pathogen Salmonella Typhimurium can stimulate innate immune responses in cultured epithelial cells by mechanisms that do not involve receptors of the innate immune system. Instead, S. Typhimurium stimulates these responses by delivering through its type III secretion system the bacterial effector proteins SopE, SopE2, and SopB, which in a redundant fashion stimulate Rho-family GTPases leading to the activation of mitogen-activated protein (MAP) kinase and NF-κB signaling. These observations have implications for the understanding of the mechanisms by which Salmonella Typhimurium induces intestinal inflammation as well as other intestinal inflammatory pathologies

Ethanolamine Transport in Human Placental Brush-Border Membrane Vesicles

ABSTRACT Pathways for transport of ethanolamine by human placental epithelia were investigated by measurement of [ 3 H]ethanolamine uptake in brush-border membrane vesicles isolated by divalent cation precipitation. The presence of a conductive uptake pathway for ethanolamine was suggested by the marked stimulation of ethanolamine uptake to levels exceeding equilibrium induced by an inside-negative potassium diffusion potential. Evidence to suggest conductive ethanolamine uptake resulted from a mediated transport process included 1) the concentration-dependent inhibition by choline; 2) trans-stimulation of choline and ethanolamine uptake by ethanolamine; and 3) substrate-specific inhibition by chemically related analogs. Transport of both choline and ethanolamine by a common facilitated diffusion mechanism is suggested by 1) trans-stimulation of choline uptake by ethanolamine; 2) mutual inhibition of conductive choline and ethanolamine uptake by ethanolamine and choline; 3) the effect of ethanolamine on the kinetics of conductive choline uptake; and 4) the rank order inhibition of choline and ethanolamine uptake by the same panel of chemical analogs. The present study identifies the presence of a facilitated diffusion mechanism as a brush-border membrane transport pathway for choline and ethanolamine accumulation by human placenta