SIC-POVMs and the Extended Clifford Group

We describe the structure of the extended Clifford Group (defined to be the group consisting of all operators, unitary and anti-unitary, which normalize the generalized Pauli group (or Weyl-Heisenberg group as it is often called)). We also obtain a number of results concerning the structure of the Clifford Group proper (i.e. the group consisting just of the unitary operators which normalize the generalized Pauli group). We then investigate the action of the extended Clifford group operators on symmetric informationally complete POVMs (or SIC-POVMs) covariant relative to the action of the generalized Pauli group. We show that each of the fiducial vectors which has been constructed so far (including all the vectors constructed numerically by Renes et al) is an eigenvector of one of a special class of order 3 Clifford unitaries. This suggests a strengthening of a conjuecture of Zauner's. We give a complete characterization of the orbits and stability groups in dimensions 2-7. Finally, we show that the problem of constructing fiducial vectors may be expected to simplify in the infinite sequence of dimensions 7, 13, 19, 21, 31,... . We illustrate this point by constructing exact expressions for fiducial vectors in dimensions 7 and 19.Comment: 27 pages. Version 2 contains some additional discussion of Zauner's original conjecture, and an alternative, possibly stronger version of the conjecture in version 1 of this paper; also a few other minor improvement

Pauli Diagonal Channels Constant on Axes

We define and study the properties of channels which are analogous to unital qubit channels in several ways. A full treatment can be given only when the dimension d is a prime power, in which case each of the (d+1) mutually unbiased bases (MUB) defines an axis. Along each axis the channel looks like a depolarizing channel, but the degree of depolarization depends on the axis. When d is not a prime power, some of our results still hold, particularly in the case of channels with one symmetry axis. We describe the convex structure of this class of channels and the subclass of entanglement breaking channels. We find new bound entangled states for d = 3. For these channels, we show that the multiplicativity conjecture for maximal output p-norm holds for p=2. We also find channels with behavior not exhibited by unital qubit channels, including two pairs of orthogonal bases with equal output entropy in the absence of symmetry. This provides new numerical evidence for the additivity of minimal output entropy

Integrated whole transcriptome and DNA methylation analysis identifies gene networks specific to late-onset Alzheimer’s disease

Previous transcriptome studies observed disrupted cellular processes in late-onset Alzheimer\u27s disease (LOAD), yet it is unclear whether these changes are specific to LOAD, or are common to general neurodegeneration. In this study, we address this question by examining transcription in LOAD and comparing it to cognitively normal controls and a cohort of disease controls. Differential transcription was examined using RNA-seq, which allows for the examination of protein coding genes, non-coding RNAs, and splicing. Significant transcription differences specific to LOAD were observed in five genes: C10orf105, DIO2, a lincRNA, RARRES3, and WIF1. These findings were replicated in two independent publicly available microarray data sets. Network analyses, performed on 2,504 genes with moderate transcription differences in LOAD, reveal that these genes aggregate into seven networks. Two networks involved in myelination and innate immune response specifically correlated to LOAD. FRMD4B and ST18, hub genes within the myelination network, were previously implicated in LOAD. Of the five significant genes, WIF1 and RARRES3 are directly implicated in the myelination process; the other three genes are located within the network. LOAD specific changes in DNA methylation were located throughout the genome and substantial changes in methylation were identified within the myelination network. Splicing differences specific to LOAD were observed across the genome and were decreased in all seven networks. DNA methylation had reduced influence on transcription within LOAD in the myelination network when compared to both controls. These results hint at the molecular underpinnings of LOAD and indicate several key processes, genes, and networks specific to the disease

Motherhood, Moral Authority and the Charismatic Matriarch in the Aftermath of Lethal Violence

Images of maternal suffering are an evocative and powerful means of communication in a world where the private grief of victims has increasingly become subject to commodification and public consumption. This article looks at the influence of bereaved mothers as symbols of respect, peace and dignity in the aftermath of violence, and as a result their persuasive presence in family activism. Drawing upon two case studies, this article explores the importance of victims’ stories in public life and, in particular, the presence of the charismatic matriarch in creating communities of solidarity, raising awareness of harms that have previously gone unheard and prompting policy change. It considers the ‘canonical’ story of the mother in public life and concludes by arguing that more attention should be paid to victims’ stories and their influence on policy-making, politics and eventually in becoming public grievances

Classical information deficit and monotonicity on local operations

We investigate classical information deficit: a candidate for measure of classical correlations emerging from thermodynamical approach initiated in [Phys. Rev. Lett 89, 180402]. It is defined as a difference between amount of information that can be concentrated by use of LOCC and the information contained in subsystems. We show nonintuitive fact, that one way version of this quantity can increase under local operation, hence it does not possess property required for a good measure of classical correlations. Recently it was shown by Igor Devetak, that regularised version of this quantity is monotonic under LO. In this context, our result implies that regularization plays a role of "monotoniser".Comment: 6 pages, revte

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

Qubit Channels Can Require More Than Two Inputs to Achieve Capacity

We give examples of qubit channels that require three input states in order to achieve the Holevo capacity.Comment: RevTex, 5 page, 4 figures

One-mode Bosonic Gaussian channels: a full weak-degradability classification

A complete degradability analysis of one-mode Gaussian Bosonic channels is presented. We show that apart from the class of channels which are unitarily equivalent to the channels with additive classical noise, these maps can be characterized in terms of weak- and/or anti-degradability. Furthermore a new set of channels which have null quantum capacity is identified. This is done by exploiting the composition rules of one-mode Gaussian maps and the fact that anti-degradable channels can not be used to transfer quantum information.Comment: 23 pages, 3 figure

Extending additivity from symmetric to asymmetric channels

We prove a lemma which allows one to extend results about the additivity of the minimal output entropy from highly symmetric channels to a much larger class. A similar result holds for the maximal output $p$-norm. Examples are given showing its use in a variety of situations. In particular, we prove the additivity and the multiplicativity for the shifted depolarising channel.Comment: 8 pages. This is the latest version of the first half of the original paper. The other half will appear in another pape

Cytoplasmic p53 couples oncogene-driven glucose metabolism to apoptosis and is a therapeutic target in glioblastoma.

Cross-talk among oncogenic signaling and metabolic pathways may create opportunities for new therapeutic strategies in cancer. Here we show that although acute inhibition of EGFR-driven glucose metabolism induces only minimal cell death, it lowers the apoptotic threshold in a subset of patient-derived glioblastoma (GBM) cells. Mechanistic studies revealed that after attenuated glucose consumption, Bcl-xL blocks cytoplasmic p53 from triggering intrinsic apoptosis. Consequently, targeting of EGFR-driven glucose metabolism in combination with pharmacological stabilization of p53 with the brain-penetrant small molecule idasanutlin resulted in synthetic lethality in orthotopic glioblastoma xenograft models. Notably, neither the degree of EGFR-signaling inhibition nor genetic analysis of EGFR was sufficient to predict sensitivity to this therapeutic combination. However, detection of rapid inhibitory effects on [18F]fluorodeoxyglucose uptake, assessed through noninvasive positron emission tomography, was an effective predictive biomarker of response in vivo. Together, these studies identify a crucial link among oncogene signaling, glucose metabolism, and cytoplasmic p53, which may potentially be exploited for combination therapy in GBM and possibly other malignancies