Abstract
We discuss the procedure of different partitions in the finite set of N integer numbers and construct generic formulas for a bijective map of real numbers s y , where y = 1, 2,…, N, N = \( \underset{k=1}{\overset{n}{\varPi}}{X}_k, \) and X k are positive integers, onto the set of numbers s(y(x 1, x 2,…, x n )). We give the functions used to present the bijective map, namely, y(x 1, x 2, …, x n ) and x k (y) in an explicit form and call them the functions detecting the hidden correlations in the system. The idea to introduce and employ the notion of “hidden gates” for a single qudit is proposed. We obtain the entropic-information inequalities for an arbitrary finite set of real numbers and consider the inequalities for arbitrary Clebsch–Gordan coefficients as an example of the found relations for real numbers.
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Man’ko, V.I., Seilov, Z. The Partition Formalism and New Entropic-Information Inequalities for Real Numbers on an Example of Clebsch–Gordan Coefficients. J Russ Laser Res 38, 50–60 (2017). https://doi.org/10.1007/s10946-017-9619-7
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DOI: https://doi.org/10.1007/s10946-017-9619-7