Wigner functions, negativity volumes, and experimental generation of Pegg-Barnett phase-operator eigenstates

TL;DR

This paper analyzes the non-Gaussian properties of Pegg-Barnett phase eigenstates via Wigner functions, proposes a quantum circuit for their generation, and explores their application in phase estimation.

Contribution

It introduces a quantum-optical circuit for generating Pegg-Barnett phase eigenstates and studies the effects of detector inefficiency on their properties and applications.

Findings

Eigenstates exhibit negativity in Wigner functions indicating non-Gaussianity.

The proposed circuit can generate approximate eigenstates with high fidelity.

Detector inefficiency reduces negativity volume and fidelity, affecting practical implementation.

Abstract

In this paper, we study the non-Gaussianity of the eigenstates of the Pegg-Barnett phase observable. By computing the Wigner functions of the eigenstates, we confirm that they take negative values in specific regions of the phase space. The Pegg-Barnett phase-operator eigenstates lie on a finite-dimensional Hilbert space. Thus, we examine how their negativity volumes depend on the dimension of the Hilbert space. Moreover, we present a quantum-optical circuit that generates these eigenstates and identify single-photon detection as the origin of their non-Gaussianity. To investigate a more realistic experimental implementation, we introduce imperfect single-photon detectors with non-unit efficiency into the circuit and evaluate the dependence of the detection probability, the output-ideal fidelity, and the negativity volume of the approximate eigenstate output from the circuit on the detector efficiency. Finally, as a practical application, we consider a phase-estimation experiment of an arbitrary unknown state by injecting both the unknown state and a known Pegg-Barnett eigenstate into a 50-50 beam splitter and individually counting the numbers of photons emitted from its two output ports.