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

TL;DR

This paper connects experimentally accessible witnesses of non-Gaussian features with the theoretical stellar rank measure, enabling scalable certification of non-Gaussian states in quantum systems.

Contribution

It establishes a quantitative link between non-Gaussian witnesses and stellar rank, providing lower bounds and a hierarchy of thresholds for experimental certification.

Findings

Witnesses can certify lower bounds of stellar rank.

Normalized expectation and variance witnesses form a hierarchy.

Results enable scalable certification of non-Gaussian states.

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.