Kaleidoscope of Classical Images and Quantum Coherent States

TL;DR

This paper introduces a generalized class of quantum states based on classical images and n-polygon symmetry, expanding the framework of coherent states for quantum information processing.

Contribution

It develops a new family of kaleidoscope coherent states related to n-polygon symmetry, connecting them with quantum groups and Fourier transforms for qudit applications.

Findings

States can be generated via Quantum Fourier transform

States relate to quantum groups and q-calculus

Potential for qudits in quantum information

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.