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arXiv · 2603.03185

Witnesses of non-Gaussian features as lower bounds of stellar rank

Jan Provazník·Šimon Bräuer·Vojtěch Kala·Jaromír Fiurášek·Petr Marek
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Abstract

Quantum non-Gaussian states and operations serve as fundamental resources for universal quantum computation, error correction, and high-precision metrology, extending beyond the Gaussian limits. While the stellar rank provides a rigorous hierarchical measure of non-Gaussianity, it remains challenging to determine experimentally. Conversely, witnesses of non-Gaussian features, based on the expectation values and variances of measurable observables, offer an accessible method for certifying non-Gaussian behavior but lack a direct connection to stellar rank. In this work, we establish a quantitative connection between these witnesses and stellar rank, demonstrating that the former can provide certifiable lower bounds on stellar rank. We introduce normalized expectation value and variance-based quantifiers and show that these witnesses form a consistent hierarchy of thresholds corresponding to stellar rank. Our results bridge the gap between abstract hierarchical measures and experimentally accessible quantifiers, enabling scalable certification of non-Gaussian states.

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Jan Provazník, Šimon Bräuer, Vojtěch Kala, Jaromír Fiurášek, Petr Marek. 2026-03-03. Witnesses of non-Gaussian features as lower bounds of stellar rank. https://arxiv.org/abs/2603.03185

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