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Kaleidoscope of Classical Vortex Images and Quantum Coherent States

  • Oktay K. Pashaev
  • Aygül KoçakEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 266)

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.

Keywords

Coherent states Quantum information Qubit Qutrit Qudit Quantum Fourier transform 

Notes

Acknowledgements

This work is supported by TUBITAK grant 116F206.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsIzmir Institute of TechnologyIzmirTurkey

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