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

Man’ko, Vladimir I.; Seilov, Z.

doi:10.1007/s10946-017-9619-7

Cited by 8 publications

(4 citation statements)

References 33 publications

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“…In our work [24] we introduced the approach of dividing one system into few subsystems, i.e. representing variable n in terms of few variables n(x 1 , x 2 , ..).…”

Section: Correlations In Vibronic Repetitions In Electron Line Intens...mentioning

confidence: 99%

Universal information-entropic inequalities for Franck-Condon factors of diatomic molecules

Man’ko¹,

Seilov²

2019

Preprint

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New entropic inequalities are obtained for Franck-Condon factors (FCF-s) of diatomic molecules in adiabatic harmonic oscillator approximation. The probability distributions associated with FCF-s of diatomic molecules are presented in the form of joint-probability distributions of either two or three random variables. In view of this representation information inequalities corresponding to subadditivity condition is found and in case of harmonic oscillator approximation is obtained in explicit form of new inequalities for Hermite polynomials. Physical meaning of obtained entropicinformation inequalities as characteristics of hidden correlations in vibronic spectra of the molecules is studied.

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“…In our work [24] we introduced the approach of dividing one system into few subsystems, i.e. representing variable n in terms of few variables n(x 1 , x 2 , ..).…”

Section: Correlations In Vibronic Repetitions In Electron Line Intens...mentioning

confidence: 99%

Universal information-entropic inequalities for Franck-Condon factors of diatomic molecules

Man’ko¹,

Seilov²

2019

Preprint

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“…, (n 1 , n 2 ), where N = n 1 n 2 . This map can be described by the functions discussed in [42][43][44].…”

Section: Bayes' Formula For the Probability Distribution Of One Randomentioning

confidence: 99%

“…where functions n(j, k), j(n), and k(n) are constructed in [44]. The relation of the joint probability distribution P(j, k) to the marginal probability distributions corresponds to the presence of correlations in the system with two random variables.…”

Section: Bayes' Formula For the Probability Distribution Of One Randomentioning

confidence: 99%

New Entropic Inequalities and Hidden Correlations in Quantum Suprematism Picture of Qudit States

Man’ko

2018

Entropy

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We study an analog of Bayes' formula and the nonnegativity property of mutual information for systems with one random variable. For single-qudit states, we present new entropic inequalities in the form of the subadditivity and condition corresponding to hidden correlations in quantum systems. We present qubit states in the quantum suprematism picture, where these states are identified with three probability distributions, describing the states of three classical coins, and illustrate the states by Triada of Malevich's squares with areas satisfying the quantum constraints. We consider arbitrary quantum states belonging to N-dimensional Hilbert space as (N 2 − 1) fair probability distributions describing the states of (N 2 − 1) classical coins. We illustrate the geometrical properties of the qudit states by a set of Triadas of Malevich's squares. We obtain new entropic inequalities for matrix elements of an arbitrary density N×N-matrix of qudit systems using the constructed maps of the density matrix on a set of the probability distributions. In addition, to construct the bijective map of the qudit state onto the set of probabilities describing the positions of classical coins, we show that there exists a bijective map of any quantum observable onto the set of dihotomic classical random variables with statistics determined by the above classical probabilities. Finally, we discuss the physical meaning and possibility to check derived inequalities in the experiments with superconducting circuits based on Josephson junction devices.

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“…It is worth noting that analogous functions were discussed in [33,34]. In the case where the integer N is the product of three integers N = X 1 X 2 X 3 , we introduce the functions y(x 1 , x 2 , x 3 ), x 1 (y), x 2 (y), and x 3 (y) given by the expressions [31]…”

Section: The Functions Detecting the Hidden Correlationsmentioning

confidence: 99%

Conditional Information and Hidden Correlations in Single-qudit States

Man’ko

2017

J Russ Laser Res

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We discuss the notions of mutual information and conditional information for noncomposite systems, classical and quantum; both the mutual information and the conditional information are associated with the presence of hidden correlations in the state of a single qudit. We consider analogs of the entanglement phenomena in the systems without subsystems related to strong hidden quantum correlations.

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

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 = n k=1

Cited by 8 publications

References 33 publications

Universal information-entropic inequalities for Franck-Condon factors of diatomic molecules

Universal information-entropic inequalities for Franck-Condon factors of diatomic molecules

New Entropic Inequalities and Hidden Correlations in Quantum Suprematism Picture of Qudit States

Conditional Information and Hidden Correlations in Single-qudit States

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