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

TL;DR

This paper explores the application of Wigner functions for the angle and orbital angular momentum pair to quantum information, analyzing properties of entangled states and their potential use in quantum experiments.

Contribution

It extends the framework of Wigner functions to quantum information concepts like qubits and entangled states, highlighting their unique topological features.

Findings

Wigner functions of Bell states have a twisted topology on the phase space.

Properties of superposed states' Wigner functions are characterized and visualized.

Potential applications in quantum optics and electron beam experiments are discussed.

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.