Wigner function of a qubit

TL;DR

This paper introduces a geometric quantization method for qubits using the real polarization approach, enabling the construction of wave functions and Wigner functions in both position and momentum representations, with applications in quantum informatics.

Contribution

It presents a novel geometric quantization technique for spin systems that allows explicit construction of qubit wave functions and Wigner functions.

Findings

Constructed qubit wave functions in position and momentum spaces

Derived the Wigner function for a qubit using geometric quantization

Potential applications in quantum information processing

Abstract

We show that real polarization method can be effectively used to geometrically quantize physical systems with compact phase space, like the spin. Our method enables us to construct a wave function of a qubit in both position and momentum representations and also its Wigner function. These results can be used in quantum informatics.