Non-adaptive Measurement-based Quantum Computation and Multi-party Bell Inequalities

Quantum correlations exhibit behaviour that cannot be resolved with a local hidden variable picture of the world. In quantum information, they are also used as resources for information processing tasks, such as Measurement-based Quantum Computation (MQC). In MQC, universal quantum computation can be achieved via adaptive measurements on a suitable entangled resource state. In this paper, we look at a version of MQC in which we remove the adaptivity of measurements and aim to understand what computational abilities still remain in the resource. We show that there are explicit connections between this model of computation and the question of non-classicality in quantum correlations. We demonstrate this by focussing on deterministic computation of Boolean functions, in which natural generalisations of the Greenberger-Horne-Zeilinger (GHZ) paradox emerge; we then explore probabilistic computation, via which multipartite Bell Inequalities can be defined. We use this correspondence to define families of multi-party Bell inequalities, which we show to have a number of interesting contrasting properties.Comment: 13 pages, 4 figures, final version accepted for publicatio

Housekeeping genes for phylogenetic analysis of eutherian relationships

The molecular relationship of placental mammals has attracted great interest in recent years. However, 2 crucial and conflicting hypotheses remain, one with respect to the position of the root of the eutherian tree and the other the relationship between the orders Rodentia, Lagomorpha (rabbits, hares), and Primates. Although most mitochondrial (mt) analyses have suggested that rodents have a basal position in the eutherian tree, some nuclear data in combination with mt-rRNA genes have placed the root on the so-called African clade or on a branch that includes this clade and the Xenarthra (e.g., anteater and armadillo). In order to generate a new and independent set of molecular data for phylogenetic analysis, we have established cDNA sequences from different tissues of various mammalian species. With this in mind, we have identified and sequenced 8 housekeeping genes with moderately fast rate of evolution from 22 placental mammals, representing I I orders. In order to determine the root of the eutherian tree, the same genes were also sequenced for 3 marsupial species, which were used as outgroup. Inconsistent with the analyses of nuclear + mt-rRNA gene data, the current data set did not favor a basal position of the African clade or Xenarthra in the eutherian tree. Similarly, by joining rodents and lagomorphs on the same basal branch (Glires hypothesis), the data set is also inconsistent with the tree commonly favored in mtDNA analyses. The analyses of the currently established sequences have helped examination of problematic parts in the eutherian tree at the same time as they caution against suggestions that have claimed that basal eutherian relationships have been conclusively settled