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

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 are defined in 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. We then examine how the detection probability, the output-ideal fidelity, and the negativity volume of the approximate eigenstate output from the circuit change with 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.

17 pages, 9 figures, latex2e; v2: The calculation errors in Figs. 4, 5, 6 and Eq. (27) have been corrected

arXiv:2604.23086 [quant-ph]

(or arXiv:2604.23086v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2604.23086 Focus to learn more arXiv-issued DOI via DataCite

J. Phys. D: Appl. Phys. 59, 345103 (2026)

https://doi.org/10.1088/1361-6463/ae97f0 Focus to learn more DOI(s) linking to related resources

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