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Quantum Correlation
In quantum mechanics, quantum correlation is the expected value of the product of the alternative outcomes. In other words, it is the expected change in physical characteristics as one quantum system passes through an interaction site. In John Bell's 1964 paper that inspired the Bell test, it was assumed that the outcomes A and B could each only take one of two values, -1 or +1. It followed that the product, too, could only be -1 or +1, so that the average value of the product would be :\frac where, for example, N++ is the number of simultaneous instances ("coincidences") of the outcome +1 on both sides of the experiment. However, in actual experiments, detectors are not perfect and produce many null outcomes. The correlation can still be estimated using the sum of coincidences, since clearly zeros do not contribute to the average, but in practice, instead of dividing by Ntotal, it is customary to divide by :N_ + N_+ N_ + N_ the total number of observed coincidences. The le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale. Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values ( quantization); objects have characteristics of both particles and waves (wave–particle duality); and there are limits to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Value
In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a large number of independently selected outcomes of a random variable. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration. The expected value of a random variable is often denoted by , , or , with also often stylized as or \mathbb. History The idea of the expected value originated in the middle of the 17th century from the study of the so-called problem of points, which seeks to divide the stakes ''in a fair way'' between two players, who have to end th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Stewart Bell
John Stewart Bell FRS (28 July 1928 – 1 October 1990) was a physicist from Northern Ireland and the originator of Bell's theorem, an important theorem in quantum physics regarding hidden-variable theories. In 2022, the Nobel Prize in Physics was awarded to Alain Aspect, John Clauser, and Anton Zeilinger for work on Bell inequalities and the experimental validation of Bell's theorem. Biography Early life and work Bell was born in Belfast, Northern Ireland. When he was 11 years old, he decided to be a scientist, and at 16 graduated from Belfast Technical High School. Bell then attended the Queen's University of Belfast, where, in 1948, he obtained a bachelor's degree in experimental physics and, a year later, a bachelor's degree in mathematical physics. He went on to complete a Ph.D. in physics at the University of Birmingham in 1956, specialising in nuclear physics and quantum field theory. In 1954, he married Mary Ross, also a physicist, whom he had met while working ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bell Test
A Bell test, also known as Bell inequality test or Bell experiment, is a real-world physics experiment designed to test the theory of quantum mechanics in relation to Albert Einstein's concept of Local realism#Local realism, local realism. Named for John Stewart Bell, the experiments test whether or not the real world satisfies local realism, which requires the presence of some local hidden-variable theory, additional local variables (called "hidden" because they are not a feature of quantum theory) to explain the behavior of particles like photons and electrons. To date, all Bell tests have found that the hypothesis of local hidden variables is inconsistent with the way that physical systems behave. According to Bell's theorem, if nature actually operates in accord with any theory of local hidden variables, then the results of a Bell test will be constrained in a particular, quantifiable way. If a Bell experiment is performed and the results are ''not'' thus constrained, then th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hidden Variable Theory
In physics, hidden-variable theories are proposals to provide explanations of quantum mechanical phenomena through the introduction of (possibly unobservable) hypothetical entities. The existence of fundamental indeterminacy for some measurements is assumed as part of the mathematical formulation of quantum mechanics; moreover, bounds for indeterminacy can be expressed in a quantitative form by the Heisenberg uncertainty principle. Most hidden-variable theories are attempts to avoid quantum indeterminacy, but possibly at the expense of requiring the existence of nonlocal interactions. Albert Einstein objected to aspects of quantum mechanics, and famously declared "I am convinced God does not play dice". Einstein, Podolsky, and Rosen argued by assuming local causality that quantum mechanics is an incomplete description of reality. Bell's theorem and subsequent experiments would later show that local hidden variables (a way for finding a complete description of reality) of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistic
A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypothesis. The average (or mean) of sample values is a statistic. The term statistic is used both for the function and for the value of the function on a given sample. When a statistic is being used for a specific purpose, it may be referred to by a name indicating its purpose. When a statistic is used for estimating a population parameter, the statistic is called an ''estimator''. A population parameter is any characteristic of a population under study, but when it is not feasible to directly measure the value of a population parameter, statistical methods are used to infer the likely value of the parameter on the basis of a statistic computed from a sample taken from the population. For example, the sample mean is an unbiased estimator of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CHSH Inequality
In physics, the CHSH inequality can be used in the proof of Bell's theorem, which states that certain consequences of entanglement in quantum mechanics can not be reproduced by local hidden-variable theories. Experimental verification of the inequality being violated is seen as confirmation that nature cannot be described by such theories. CHSH stands for John Clauser, Michael Horne, Abner Shimony, and Richard Holt, who described it in a much-cited paper published in 1969. They derived the CHSH inequality, which, as with John Stewart Bell's original inequality, is a constraint on the statistical occurrence of "coincidences" in a Bell test which is necessarily true if there exist underlying local hidden variables, an assumption that is sometimes termed local realism. It is in fact the case that the inequality is routinely violated by modern experiments in quantum mechanics. Statement The usual form of the CHSH inequality is where ''a'' and ''a''′ are detector setti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Local Realism
In physics, the principle of locality states that an object is influenced directly only by its immediate surroundings. A theory that includes the principle of locality is said to be a "local theory". This is an alternative to the concept of instantaneous "action at a distance". Locality evolved out of the field theories of classical physics. The concept is that for an action at one point to have an influence at another point, something in the space between those points must mediate the action. To exert an influence, something, such as a wave or particle, must travel through the space between the two points, carrying the influence. The special theory of relativity limits the speed at which all such influences can travel to the speed of light, c. Therefore, the principle of locality implies that an event at one point cannot cause a simultaneous result at another point. An event at point A cannot cause a result at point B in a time less than T=D/c, where D is the distance between ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Local Hidden-variable Theory
In the interpretation of quantum mechanics, a local hidden-variable theory is a hidden-variable theory that satisfies the condition of being consistent with local realism. This includes all types of the theory that attempt to account for the probabilistic features of quantum mechanics by the mechanism of underlying inaccessible variables, with the additional requirement from local realism that distant events be independent, ruling out ''instantaneous'' (that is, faster-than-light) interactions between separate events. The mathematical implications of a local hidden-variable theory in regard to the phenomenon of quantum entanglement were explored by physicist John Stewart Bell, who in 1964 proved that broad classes of local hidden-variable theories cannot reproduce the correlations between measurement outcomes that quantum mechanics predicts. The most notable exception is superdeterminism. Superdeterministic hidden-variable theories can be local and yet be compatible with observati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Correlation Does Not Imply Causation
The phrase "correlation does not imply causation" refers to the inability to legitimately deduce a cause-and-effect relationship between two events or variables solely on the basis of an observed association or correlation between them. The idea that "correlation implies causation" is an example of a questionable-cause logical fallacy, in which two events occurring together are taken to have established a cause-and-effect relationship. This fallacy is also known by the Latin phrase ''cum hoc ergo propter hoc'' ('with this, therefore because of this'). This differs from the fallacy known as ''post hoc ergo propter hoc'' ("after this, therefore because of this"), in which an event following another is seen as a necessary consequence of the former event, and from conflation, the errant merging of two events, ideas, databases, etc., into one. As with any logical fallacy, identifying that the reasoning behind an argument is flawed does not necessarily imply that the resulting con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
EPR Paradox
EPR may refer to: Science and technology * EPR (nuclear reactor), European Pressurised-Water Reactor * EPR paradox (Einstein–Podolsky–Rosen paradox), in physics * Earth potential rise, in electrical engineering * East Pacific Rise, a mid-oceanic ridge * Electron paramagnetic resonance * Engine pressure ratio,of a jet engine * Ethylene propylene rubber * Yevpatoria RT-70 radio telescope (Evpatoria planetary radar) * Bernays–Schönfinkel class or effectively propositional, in mathematical logic * Endpoint references in Web addressing * Ethnic Power Relations, dataset of ethnic groups * ePrivacy Regulation (ePR), proposal for the regulation of various privacy-related topics, mostly in relation to electronic communications within the European Union Medicine * Enhanced permeability and retention effect, a controversial concept in cancer research * Emergency Preservation and Resuscitation, a medical procedure * Electronic patient record Environment * UNECE Environmental Perform ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
