Kaleidoscope of classical vortex images and quantum coherent states

DOI10.1007/978-3-030-01376-9_10zbMATH Open1418.81014arXiv1802.04620OpenAlexW2898734647MaRDI QIDQ2313103

Aygül Koçak, Oktay K. Pashaev

Publication date: 18 July 2019

Abstract: The Schr"odinger 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. The cases of the trinity states and the quartet states are described in details. Normalization formula for these states requires introduction of specific combinations of exponential functions with mod 3 and mod 4 symmetry. We show that these states can be generated for an arbitrary $n$ by the Quantum Fourier transform and can provide qutrits, ququats and in general, qudit units of quantum information. Relations of our states with quantum groups and quantum calculus are discussed.

Full work available at URL: https://arxiv.org/abs/1802.04620

zbMATH Keywords

coherent statesquantum informationquantum Fourier transformqubitqutritqudit

Mathematics Subject Classification ID

Numerical methods for discrete and fast Fourier transforms (65T50) Coherent states (81R30) Congruences; primitive roots; residue systems (11A07) Quantum coherence, entanglement, quantum correlations (81P40) Orthogonal polynomials and functions associated with root systems (33C52) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)

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