Non-Gaussianity from Superselection Rules
Abstract
The quantum theory of the electromagnetic field enables the description of multiphoton states exhibiting nonclassical statistical properties, often reflected in non-Gaussian phase-space distributions. While non-Gaussianity alone does not fully characterize quantum states, several classifications have been proposed to hierarchize non-Gaussian states according to physically or informationally relevant resources. Here, we provide a physical interpretation of non-Gaussianity and connect it to a computational perspective by showing how a prominent classification—the stellar rank—emerges as a limiting case of the roots of polynomials that univocally represent bosonic states defined with a quantized phase reference, namely the Majorana polynomials. A direct consequence of our results is a revised interpretation of both the stellar rank and non-Gaussianity itself: when superselection rules are properly taken into account, quadrature non-Gaussianity—and nonzero stellar rank—act as witnesses of particle entanglement, rather than being linked with photon addition to Gaussian states as previously assumed. In addition, we show that, because the stellar rank depends on a specific choice of coherent states, its relation to computational resources and potential quantum advantage is inherently basis dependent, being naturally tied to quadrature eigenstates as the computational basis. Motivated by this observation, we generalize the notion of stellar rank to arbitrary computational bases, thereby establishing it as a genuine witness of bosonic resources that may enable quantum advantage.
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BibTeX
@article{moulonguet2026nongaussianity,
title = {{Non-Gaussianity from Superselection Rules}},
author = {Nicolas Moulonguet and Éloi Descamps and José Lorgeré and Astghik Saharyan and Arne Keller and Pérola Milman},
journal = {Physical Review Letters},
year = {2026},
month = jul,
doi = {10.1103/5fl9-89j4},
eprint = {2603.20810},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05828955v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Non-Gaussianity from Superselection Rules
AU - Nicolas Moulonguet
AU - Éloi Descamps
AU - José Lorgeré
AU - Astghik Saharyan
AU - Arne Keller
AU - Pérola Milman
PY - 2026
DA - 2026/07/29
JO - Physical Review Letters
DO - 10.1103/5fl9-89j4
UR - https://hal.science/hal-05828955v1
AB - The quantum theory of the electromagnetic field enables the description of multiphoton states exhibiting nonclassical statistical properties, often reflected in non-Gaussian phase-space distributions. While non-Gaussianity alone does not fully characterize quantum states, several classifications have been proposed to hierarchize non-Gaussian states according to physically or informationally relevant resources. Here, we provide a physical interpretation of non-Gaussianity and connect it to a computational perspective by showing how a prominent classification—the stellar rank—emerges as a limiting case of the roots of polynomials that univocally represent bosonic states defined with a quantized phase reference, namely the Majorana polynomials. A direct consequence of our results is a revised interpretation of both the stellar rank and non-Gaussianity itself: when superselection rules are properly taken into account, quadrature non-Gaussianity—and nonzero stellar rank—act as witnesses of particle entanglement, rather than being linked with photon addition to Gaussian states as previously assumed. In addition, we show that, because the stellar rank depends on a specific choice of coherent states, its relation to computational resources and potential quantum advantage is inherently basis dependent, being naturally tied to quadrature eigenstates as the computational basis. Motivated by this observation, we generalize the notion of stellar rank to arbitrary computational bases, thereby establishing it as a genuine witness of bosonic resources that may enable quantum advantage.
SN - 0031-9007
SN - 1079-7114
ER -