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[5] [6] Consequently, the term "Bell inequality" can mean any one of a number of inequalities satisfied by local hidden-variables theories; in practice, many present-day experiments employ the CHSH inequality. All these inequalities, like the original devised by Bell, express the idea that assuming local realism places restrictions on the ...
The Leggett–Garg inequality, [1] named for Anthony James Leggett and Anupam Garg, is a mathematical inequality fulfilled by all macrorealistic physical theories.Here, macrorealism (macroscopic realism) is a classical worldview defined by the conjunction of two postulates, of which the second has actually nothing to do with “macro-realism”: [1]
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the nature of measurement.
The Atkinson index is defined as: (, …,) = {(=) / (=) / = (,...,) = +where is individual income (i = 1, 2, ..., N) and is the mean income.. In other words, the Atkinson index is the complement to 1 of the ratio of the Hölder generalized mean of exponent 1−ε to the arithmetic mean of the incomes (where as usual the generalized mean of exponent 0 is interpreted as the geometric mean).
where = is the reduced Planck constant.. The quintessentially quantum mechanical uncertainty principle comes in many forms other than position–momentum. The energy–time relationship is widely used to relate quantum state lifetime to measured energy widths but its formal derivation is fraught with confusing issues about the nature of time.
In diametrical contrast, in the case of quantum physics, the theorems of Kochen and Specker, [5] the inequalities of John Bell, [6] and experimental evidence of Alain Aspect, [7] [8] all indicate that quantum randomness does not stem from any such physical information. In 2008, Tomasz Paterek et al. provided an explanation in mathematical ...
Quantum inequalities [1] are local constraints on the magnitude and extent of distributions of negative energy density in space-time. Initially conceived to clear up a long-standing problem in quantum field theory (namely, the potential for unconstrained negative energy density at a point), quantum inequalities have proven to have a diverse range of applications.
In information theory, Pinsker's inequality, named after its inventor Mark Semenovich Pinsker, is an inequality that bounds the total variation distance (or statistical distance) in terms of the Kullback–Leibler divergence. The inequality is tight up to constant factors.