Wigner functions for the pair angle and orbital angular momentum: Possible applications in quantum information

Abstract

The framework of Wigner functions for the canonical pair angle and orbital angular momentum, derived and analyzed in 2 recent papers [H. A. Kastrup, Phys.Rev. A 94, 062113(2016) and Phys.Rev. A 95, 052111(2017)] is applied to elementary concepts of quantum information like qubits and 2-qubits, e.g., entangled EPR/Bell states etc. Properties of the associated Wigner functions of such superposed states (pure and mixed) are discussed and illustrated. The Wigner functions of ERP/Bell states are distinguished by their topologically "twisted" domain on the configuration subspace S^1xS^1, a torus, of the total phase space. Like the applications of Wigner functions in quantum optics the results presented in the present paper may be useful for the description and analysis of quantum information experiments with orbital angular momenta of light beams or electron beams, respectively.