In quantum information theory, quantum relative entropy is a measure of distinguishability between two quantum states. It is the quantum mechanical analog of relative entropy.
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In the album, the song starts off with a flute melody, but starts with vocals directly on the show. The track later segues into "The Fire Ballet". Originally, the song had a lot of problems with lyric distinguishability. The most significant one, was the opening line.
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In quantum mechanics, and especially quantum information and the study of open quantum systems, the trace distance T is a metric on the space of density matrices and gives a measure of the distinguishability between two states. It is the quantum generalization of the Kolmogorov distance for classical probability distributions.
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Existence and uniqueness for electrode models for electric current computed tomography. SIAM Journal on Applied Mathematics, 52(4), 1023–1040.Cheney, M., & Isaacson, D. (1992). Distinguishability in impedance imaging. Biomedical Engineering, IEEE Transactions on, 39(8), 852–860. See also the work published in 1992 from the Glenfield Hospital Project (reference missing).
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She has provided a new interpretation of the Bekenstein bound using relative entropy and distinguishability of states. Interlacing entropy is essential in holography, which relates quantum gravity theories to non-gravitational field theories with one less dimension. Interlacing is necessary to explain the connectivity of space and to describe physics beyond the event horizon.
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To establish violation of the principle of complementarity, Afshar considers the case in which both pinholes are open and asserts both high visibility V of interference as well as high distinguishability D (corresponding to which-path information), so that V2 \+ D2 > 1. His claim depends heavily on whether which-path information is preserved when both pinholes are open.
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However, this is not structurally economical, and tripartite systems are comparatively rare, but to have all arguments marked the same makes the arguments too ambiguous. Alongside the principle of distinguishability seems to operate a principle of economy. It is more efficient to have as few cases as possible without compromising intelligibility. In this way the dual pressures of efficiency and economy have produced a system which patterns two kinds of arguments together a third separately.
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This relation involves correctly guessing which of the two paths the particle would have taken, based on the initial preparation. Here P can be called the predictability. A year later Englert, in 1996, derived a related relation which dealt with experimentally acquiring knowledge of the two paths using an apparatus, as opposed to predicting the path based on initial preparation This relation is D^2+ V^2\le 1 \, . Here D is called the distinguishability.
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The information basis for creation ex nihilo. According to John von Neumann, starting trivially from an empty set of numbers an infinite sequence of numbers can bootstrap their way out. An empty set creates the number 1 by observing an empty set within itself which is enough of a basis for distinguishability. It creates the number 2 by observing an empty set within the second empty set and the number 1, and so on.
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In quantum information, the diamond norm is a distance metric between quantum operations. Informally, the diamond norm measures the "single use distinguishability" of the operations. If a player is randomly given one of two operations, permitted to pass one state through the unknown operation, and then measures the state in an attempt to determine which operation they were given, then the amount that such a player can bias their success probability away from 0.5 is proportional to the diamond norm between the two operations.
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But from a specifically thermodynamic viewpoint, it is not paradoxical, because in that discipline the degree of constitutive difference is not questioned; it is either there or not there. Gibbs himself did not see it as paradoxical. Distinguishability of two materials is a constitutive, not a thermodynamic, difference, for the laws of thermodynamics are the same for every material, while their constitutive characteristics are diverse.Truesdell, C. (1969). Rational Thermodynamics: a Course of Lectures on Selected Topics, McGraw-Hill Book Company, New York, p. 6.
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This species, found in present-day Pennsylvania, was originally described by J. Leidy in 1856. As mentioned above, there is much debate regarding the distinguishability between B. nitida and B. virginiensis, however based on evidence presented by Weems (2004), there are several distinguishable traits specific to each species. B. nitida has a maximum headshield length of , a narrow and shallow trifid preorbital recess, has an anterior-median-dorsal (AMD) plate that is wider than it is long and a ventral thoracic shield that has convex lateral borders.
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Natanson was head of Theoretical Physics at Kraków University from 1899 to 1935. Theoretical Physics in Poland Before 1939, Retrieved March 29, 2010 He published a series of papers on thermodynamically irreversible processes, gaining him recognition in the rapidly growing field. He was the first to consider the distinguishability of photons in the statistical analysis of elementary processes, a precursor of the concept of quantum indistinguishability. He discovered a quantum statistics, rediscovered 11 years later by Satyendra Nath Bose and generalized by Albert Einstein – the Bose–Einstein statistics.
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A physically motivated scenario to be addressed is the unwanted introduction of distinguishability between photons, which destroys quantum interference (this regime is readily accessible experimentally, for example by introducing temporal delay between photons). The opportunity then exists to tune between ideally indistinguishable (quantum) and perfectly distinguishable (classical) data and measure the change in a suitably constructed metric. This scenario can be addressed by a statistical test which performs a one-on-one likelihood comparison of the output probabilities. This test requires the calculation of a small number of permanents, but does not need the calculation of the full expected probability distribution.
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The wave–particle duality relation, often loosely referred to as the Englert–Greenberger–Yasin duality relation, or the Englert–Greenberger relation, relates the visibility, V, of interference fringes with the definiteness, or distinguishability, D, of the photons' paths in quantum optics. As an inequality: :D^2+ V^2\le 1 \, Although it is treated as a single relation, it actually involves two separate relations, which mathematically look very similar. The first relation, derived by Greenberger and Yasin in 1988, is expressed as P^2+ V^2\le 1 \, . It was later extended by Jaeger, Shimony, and Vaidman in 1995.
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Any device designed to represent data and perform computation, regardless of the physics principles it exploits and materials used to build it, must have two fundamental properties: distinguishability and conditional change of state, the latter implying the former. This means that such a device must have barriers that make it possible to distinguish between states, and that it must have the ability to control these barriers to perform conditional change of state. For example, in a digital electronic system, transistors play the role of such controllable energy barriers, making it extremely practical to perform computing with them.
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The categorization and naming of a particular species should be regarded as a hypothesis about the evolutionary relationships and distinguishability of that group of organisms. As further information comes to hand, the hypothesis may be confirmed or refuted. Sometimes, especially in the past when communication was more difficult, taxonomists working in isolation have given two distinct names to individual organisms later identified as the same species. When two named species are agreed to be of the same species, the older species name is almost always retained dropping the newer species name honoring a convention known as "priority of nomenclature".
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The naming of a particular species, including which genus (and higher taxa) it is placed in, is a hypothesis about the evolutionary relationships and distinguishability of that group of organisms. As further information comes to hand, the hypothesis may be confirmed or refuted. Sometimes, especially in the past when communication was more difficult, taxonomists working in isolation have given two distinct names to individual organisms later identified as the same species. When two named species are discovered to be of the same species, the older species name is given priority and usually retained, and the newer name considered as a junior synonym, a process called synonymisation.
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A collector array may be used to collect millions or billions of atoms, molecules, and fine particulates by using a number of wafers made of different elements. The molecular structure of these wafers allows the collection of various sizes of particles. Collector arrays, such as those flown on Genesis, are ultra-pure in order to ensure maximal collection efficiency, durability, and analytical distinguishability. Collector arrays are useful for collecting tiny, fast-moving atoms such as those expelled by the Sun through the solar wind, but can also be used for collection of larger particles such as those found in the coma of a comet.
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Bottles have a distinctive rounded-wedge shape and are designed to stand on their caps, with the label folding over the top of the bottle, where the name of the drug is printed in large print for easy identification. A cutout on the back of the bottle includes space for a data card describing the effects and risks of the medication. Fundamental to the design is a colored rubber ring that serves as a color code so different members of a household can distinguish their individual prescriptions. An overall priority is given to distinguishability; the most important information (patient name, drug name, instructions) are placed prominently on the upper half of the label.
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Markham's storm petrel inhabits waters in the Pacific Ocean around Ecuador, Peru, and Chile, though sightings have occurred on the equator west of the Galápagos Islands, within the Panama Bight, and off of Baja California. Sightings off of Baja California might mistake Markham's storm petrel for the black storm petrel due to difficulties of distinguishability in the field. Spear and Ainley (2007) observed Markham's storm petrel from to , which expanded its westward range from a compilation of sightings recorded by ornithologist Richard S. Crossin in 1974. Its presence is highly unlikely in the Atlantic Ocean outside of freak vagrancies, and in 2007, Spear and Ainley classified the species as endemic to the Humboldt Current.
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The significance of the relations is that they express quantitatively the complementarity of wave and particle viewpoints in double slit experiments. The complementarity principle in quantum mechanics, formulated by Niels Bohr, says that the wave and particle aspects of quantum objects cannot be observed at the same time. The wave–particle duality relations makes Bohr's statement more quantitative – an experiment can yield partial information about the wave and particle aspects of a photon simultaneously, but the more information a particular experiment gives about one, the less it will give about the other. The predictability P which expresses the degree of probability with which path of the particle can be correctly guessed, and the distinguishability D which is the degree to which one can experimentally acquire information about the path of the particle, are measures of the particle information, while the visibility of the fringes V is a measure of the wave information.
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Along with the single white cue ball, plain unnumbered (or sometimes ) and , seven of each colour, are used in lieu of the numbered and common to international eight-ball and other pool games. Many (especially North American) suppliers refer to the yellows-and-reds sets as "casino" balls, whether UK- or US-sized, because they were formerly used in US casino-hosted, televised, modified-rules eight-ball tournaments popular in the 1970s; the coloured rather than numbered sets were selected for their distinguishability on TV. The , however, still typically bears a number "8" (a holdover from kelly pool), though numberless variants are not unknown. British pool tables come in 6 × 3 foot (1.8 × 0.9 m) or 7 × 3.5 ft (2.12 × 1.06 m) varieties, with 7 feet being the regulation size for league play. The table has pockets just larger than the balls and rounded, as in the game of snooker, whereas the international-style (or "American- style") table has pockets significantly wider, with pointed .
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