Lower Bound on Entanglement of Formation for the Qubit-Qudit System

Wootters [PRL 80, 2245 (1998)] has derived a closed formula for the entanglement of formation (EOF) of an arbitrary mixed state in a system of two qubits. There is no known closed form expression for the EOF of an arbitrary mixed state in any system more complicated than two qubits. This paper, via a relatively straightforward generalization of Wootters' original derivation, obtains a closed form lower bound on the EOF of an arbitary mixed state of a system composed of a qubit and a qudit (a d-level quantum system, with d greater than or equal to 3). The derivation of the lower bound is detailed for a system composed of a qubit and a qutrit (d = 3); the generalization to d greater than 3 then follows readily.Comment: 14 pages, 0 Figures, 0 Table

Report of the Attorney General’s Task Force On Motor Fuel Pricing in Nebraska

In the wake of the devastation of Hurricanes Katrina and Rita, Nebraskans experienced a dramatic increase in the price of motor fuels. Although Nebraska was not impacted directly by the physical effects of these storms, damage to critical production, refining, and transportation facilities in the Gulf Coast region sent shock waves throughout the country. Attorney General Jon Bruning convened this task force for the purpose of studying these price movements and to analyze whether price-gouging activity may be occurring. Motor vehicle fuels are a vital commodity. Businesses and consumers depend on a network of oil producers, refiners, and retailers and an extensive transportation system to provide these fuels for daily use. This network extends far beyond Nebraska borders and links oil producers, refiners, retailers, and consumers across the entire globe. Careful scrutiny of the pricing and delivery of petroleum products is not a singular phenomenon limited to Nebraska. On a federal level, the Federal Trade Commission (FTC) regularly examines the petroleum industry to address concerns about concentration in production and refining and issues affecting retail pricing. Other states also have undertaken investigations, with Florida recently concluding a study addressing antitrust concerns in that state. These studies have not found violations of law, and they generally have found competitive markets affected by worldwide conditions. Growing global demand has led to increasing dependence on imported crude oil products, and disruptions in supplies–whether from political or natural causes–quickly are assimilated into market prices on a worldwide scale. This study is unique in focusing on Nebraska markets. No refineries currently operate in Nebraska. Motor fuels for sale in retail establishments in Nebraska come primarily through pipelines, which depend heavily on refinery operations in the Gulf Coast region for supplies. An extensive network of retail establishments serves Nebraska consumers and businesses, but these retailers generally can be characterized as price takers dependent upon other suppliers for their inventory. After laying a foundation for understanding national price trends, this study analyzes price data from a sample of establishments throughout different geographic regions of the state. This analysis focuses on price and gross margin behavior during a period of approximately one year, including the months immediately preceding and following Hurricanes Katrina and Rita. This study begins with a discussion of legal questions that are basic to defining price gouging. After analyzing the general principles for price determination in a market economy, Part 1 outlines legal constraints from both federal and state law that affect price-setting functions. It compares statutes from other states with Nebraska law and examines the concept of unconscionability in proscribing certain commercial behavior. It concludes that retail price behavior in Nebraska is unlikely to meet a standard of unconscionability under the current Nebraska statute. Part 2 examines U.S. Energy Information Agency data to determine factors contributing to volatility in oil and refined gasoline prices. Additionally, we investigate the profitability of twenty-one major independent oil companies during the period before and after the hurricanes struck. Part 3 examines gasoline and diesel price fluctuations in individual Nebraska cities both before and after Hurricanes Katrina and Rita struck the Gulf Coast region. We examine how prices in Nebraska react to the natural disasters in the Gulf Coast. We also examine whether any particular brands (or stations) commonly led price increases and declines in Nebraska cities

Three-dimensional stratigraphic complexity within mixed Eolian-Fluvial successions: implications for reservoir connectivity

On-going exploration of conventional hydrocarbon plays is increasingly focused towards the development of geologically complex reservoirs for which stratigraphic heterogeneity is difficult to predict. Many such current reservoirs, and an increasing proportion of likely future ones, are characterized by sedimentary bodies that accumulated as mixed eolian-fluvial systems that competed and interacted synchronously. Well-known reservoir examples include the Permian Unayzah Formation of Saudi Arabia, the Permian Rotliegend Group of the North Sea, the Triassic Ormskirk Sandstone of the East Irish Sea, the Jurassic Norphlet Sandstone of the Gulf of Mexico, and the Cretaceous Agrio Formation, Argentina. These mixed depositional systems typically exhibit highly variable lateral and vertical facies configurations that preserve complex juxtapositions of architectural elements composed of stratal units with markedly variable reservoir properties. Such stratigraphic partitioning is intrinsically difficult to predict from limited subsurface data. As such, there exists a requirement for more sophisticated geological models to better account for reservoir architecture and connectivity. This work uses outcropping case-study examples of eolian-fluvial interactions from the Triassic Sherwood Sandstone Group of the UK and the Permo-Pennsylvanian Cutler Group of southeast Utah, USA, to develop a suite of predictive models that depict common styles of stratigraphic complexity within eolian-fluvial systems. Studied successions accumulated in response to a variety of system interactions, deposits of which are preserved at a range of spatial scales from 100–104 m: (i) short-lived and localized fluvial reworking of eolian dune deposits in response to flash flood events; (ii) eolian reworking of fluvial deposits via winnowing; (iii) the fluvial exploitation and possible damming of open interdune corridors; (iv) the flooding of isolated (spatially enclosed) interdune hollows in response to an elevated water table. Identified types of interactions are characterized within a spatial scheme whereby occurrences can be used as a predictor of relative position within the larger-scale zone of transition between coeval eolian dune-field and fluvial systems. Application of this spatial scheme allows for prediction of the type of eolian-fluvial interactions expected for a range of paleogeographic settings, thereby serving as a tool for ranking exploration targets within larger prospect areas

Great Canadian Lagerstätten 3. Late Ordovician Konservat-Lagerstätten in Manitoba

Konservat-Lagerstätten, deposits in which soft-bodied or lightly sclerotized fossils are preserved, are very rare in Ordovician strata. Three significant sites are known from Upper Ordovician rocks in Manitoba: at Cat Head – McBeth Point, William Lake, and Airport Cove. These sites are in two distinct sedimentary basins: the former two are in the Williston Basin, while the latter is in the Hudson Bay Basin. All three sites contain marine fossils, but each has a different assemblage that contributes a distinct piece of the diversity picture. Important groups represented at one or more of the sites include seaweeds (algae), sponges, cnidarian medusae (jellyfish), conulariids, trilobites, eurypterids, xiphosurids (horseshoe crabs), and pycnogonids (‘sea spiders’). The different biotas reflect depositional conditions at each site. Many of the fossils are unknown elsewhere in the Ordovician at the family level or higher. The province of Manitoba therefore makes a significant contribution to knowledge of Late Ordovician biodiversity.SOMMAIRELes lagerstätten de conservation, ces sédiments contenant des fossiles d’organismes à corps mou ou légèrement sclérotisés particulièrement bien conservés, sont très rares dans les strates ordoviciennes.  Trois sites d’importance sont connus dans des roches de l'Ordovicien supérieur à Cat Head, Manitoba, soit McBeth Point, William Lake et  Airport Cove.  Ces sites sont situés dans deux bassins sédimentaires distincts : les deux premiers sont situés dans le bassin de Williston, tandis que le second est situé dans le bassin de la baie d'Hudson.  Les trois sites contiennent des fossiles marins, mais chacun présente un assemblage différent, chacun montrant une composante distincte de la diversité biologique d’alors.  Les groupes les plus importants représentés, dans un ou plusieurs de ces sites, sont les algues, les éponges, les cnidarian medusae (méduses), les conularides, les trilobites, les euryptérides, xiphosurides (limules) et pycnogonides.  Les différents biotopes reflètent les conditions de dépôt de chaque site.  Nombre de ces fossiles sont inconnus ailleurs dans l'Ordovicien, au niveau de la famille ou du taxon supérieur de la classification.  Ainsi, la province du Manitoba offre-t-elle une contribution importante à la connaissance de la biodiversité de l'Ordovicien supérieur

Be-10 age constraints on latest Pleistocene and Holocene cirque glaciation across the western United States

Paleoclimate: A rocky reworking of Holocene glaciology New dating of glacially-deposited rocks substantially revises our understanding of the waxing and waning of ice since the last glacial maximum. Glaciologists have long thought that moraines throughout the western United States represent ‘neoglacial’ advances about 6,000 years ago. Now, a multi-institution team led by Shaun Marcott at the University of Wisconsin-Madison has found — using cosmogenic isotopes — that these terminal deposits left by advancing glaciers are instead 9,000 to 15,000 years old. The research advances prior work by using absolute, not relative ages, and documents that glaciers retreated after the last glacial maximum ~ 21,000 years ago, fluctuated locally throughout much of the Holocene, and re-advanced during the Little Ice Age of a few hundred years ago. Glacial advances that might have occurred during the neoglacial were wiped away by the more extensive glaciations of the Little Ice Age