Non-Gaussianity from superselection rules

• URL: http://arxiv.org/abs/2603.20810v1
• Date: Sat, 21 Mar 2026 13:14:34 GMT
• Title: Non-Gaussianity from superselection rules
• Abstract summary: We provide a physical interpretation of non-Gaussianity and connect it to a computational perspective.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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