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arXiv · 1612.07145

The Partition Formalism and New Entropic-Information Inequalities for Real Numbers on an Example of Clebsch-Gordan Coefficients

V. I. Manko·Z. Seilov
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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 $y=1,2,\ldots,N$, $N=\prod \limits_{k=1}^{n} X_k$, and $X_k$ are positive integers, onto the set of numbers $s(y(x_1,x_2,\ldots,x_n))$. 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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V. I. Manko, Z. Seilov. 2016-12-21. The Partition Formalism and New Entropic-Information Inequalities for Real Numbers on an Example of Clebsch-Gordan Coefficients. https://arxiv.org/abs/1612.07145

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