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

• URL: http://arxiv.org/abs/2603.03185v1
• Date: Tue, 03 Mar 2026 17:44:23 GMT
• Title: Witnesses of non-Gaussian features as lower bounds of stellar rank
• Authors: Jan Provazník, Šimon Bräuer, Vojtěch Kala, Jaromír Fiurášek, Petr Marek,
• Abstract summary: Quantum non-Gaussian states and operations serve as fundamental resources for universal quantum computation.<n>Witnesses of non-Gaussian features offer an accessible method for certifying non-Gaussian behavior but lack a direct connection to stellar rank.<n>We introduce normalized expectation value and variance-based quantifiers and show that these witnesses form a consistent hierarchy of thresholds corresponding to stellar rank.
• Score: 0.2609784101826761
• License: http://creativecommons.org/licenses/by/4.0/
• 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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