Non-commutative tomography and signal processing

Mendes, R. Vilela

doi:10.1088/0031-8949/90/7/074022

Cited by 8 publications

(7 citation statements)

References 40 publications

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“…In addition, we point out that the tomographic-probability approach was applied in signal analysis [54,55] due to the descriptions of the signals by an analog of the Wigner function proposed by Ville [56]. The probability properties considered above can be used in the signal theory as well.…”

Section: Discussionmentioning

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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Section: Discussionmentioning

confidence: 99%

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

Man’ko

2018

Entropy

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“…The optical time-frequency tomogram is a particular case of the symplectic time-frequency tomogram T (X, µ, ν) of the signal S(t), where µ = cos θ and ν = sin θ. In some cases, another variations of tomographic representation, such as time-scale tomograms, frequency-scale tomograms, and time-conformal tomograms, are used [20].…”

Section: Tomographic Analysismentioning

confidence: 99%

“…In particular, it is important whereas modified time-frequency tomograms are able to capture some feature of highly non-stationary signals that are important. Finally, an interesting task to analyse how timefrequency tomograms can be measured in various applications, such as analysis of reflectometry data [19,20].…”

Section: Entropic Relationsmentioning

confidence: 99%

“…In particular, symplectic tomography protocols use a marginal probability distribution of shifted and squeezed position and momentum variables. This approach has been used in the context of time-frequency analysis [13] and time-frequency entropic analysis [14] for various types of signals, such as complex Gaussian signals [13][14][15][16][17][18] and reflectometry data [19,20]. A general analysis of the relation between time-frequency tomograms and other transformation (including wavelets) is presented in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Tomographic and entropic analysis of modulated signals-=SUP=-*-=/SUP=-

Mastiukova

Gavreev

Kiktenko

et al. 2020

Журнал Технической Физики

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We study an application of the quantum tomography framework for the time-frequency analysis of modulated signals. In particular, we calculate optical tomographic representations and Wigner-Ville distributions for signals with amplitude and frequency modulations. We also consider time-frequency entropic relations for modulated signals, which are naturally associated with the Fourier analysis. A numerical toolbox for calculating optical time-frequency tomograms based on pseudo Wigner-Ville distributions for modulated signals is provided.

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“…From this point of view there is a complete analogy with a quantum system state ψ description in different representations. We know that a quantum system state is given by a Dirac vector |ψ in a Hilbert space, which is determined by a wave function ψ(x) = x|ψ in a coordinate space (see, eg review [29]). In a momentum space this state is given by a function of momentum ψ(p) ≡ ψ p = p|ψ respectively.…”

Section: Signal Analysismentioning

confidence: 99%

Tomographic representation of ECG-signal

Belousov,

Elkin,

Man'ko

et al. 2018

Preprint

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Tomographic representation of an arbitrary nature signal is considered. Comparison of a tomographic representation and a fractional Fourier transform is carried out. Application of tomogram representation or identical to it the Radon transform for processing medical ECG signals is illustrated. The first results show that in contrast to routine Fourier analysis, the Radon transform revealed an additional information for patients with the early signs of ischemic heart disease (IHD) with respect to healthy persons.

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Non-commutative tomography and signal processing

Cited by 8 publications

References 40 publications

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

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

Tomographic and entropic analysis of modulated signals-=SUP=-*-=/SUP=-

Tomographic representation of ECG-signal

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