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Title: Kaleidoscope of classical vortex images and quantum coherent states
Authors: Pashaev, Oktay
Koçak, Aygül
Keywords: Coherent states
Quantum Fourier transform
Quantum information
Publisher: Springer
Abstract: The Schrödinger cat states, constructed from Glauber coherent states and applied for description of qubits are generalized to the kaleidoscope of coherent states, related with regular n-polygon symmetry and the roots of unity. This quantum kaleidoscope is motivated by our method of classical hydrodynamics images in a wedge domain, described by q-calculus of analytic functions with q as a primitive root of unity. First we treat in detail the trinity states and the quartet states as descriptive for qutrit and ququat units of quantum information. Normalization formula for these states requires introduction of specific combinations of exponential functions with mod 3 and mod 4 symmetry, which are known also as generalized hyperbolic functions. We show that these states can be generated for an arbitrary n by the Quantum Fourier transform and can provide in general, qudit unit of quantum information. Relations of our states with quantum groups and quantum calculus are discussed. © Springer Nature Switzerland AG 2018.
Description: 3rd International Conference on Symmetries, Differential Equations and Applications, SDEA-III 2017 -- 14 August 2018 through 17 August 2018 -- -- 220379
ISBN: 9783030013752
ISSN: 2194-1009
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

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