A trace distance-based geometric analysis of the stabilizer polytope for few-qubit systems
Abstract
Non-stabilizerness is a fundamental resource for quantum computational advantage, differentiating classically simulable circuits from those capable of universal quantum computation. Recently, non-stabilizerness has been shown to be relevant for a few qubit systems. In this work, we investigate the geometry of the stabilizer polytope in few-qubit quantum systems, using the trace distance to the stabilizer set to quantify non-stabilizerness. By randomly sampling quantum states, we analyze the distribution of non-stabilizerness for both pure and mixed states and compare the trace distance with other non-stabilizerness measures, as well as entanglement. Additionally, we give an analytical expression for the introduced quantifier, classify Bell-like inequalities corresponding to the facets of the stabilizer polytope, and establish a general concentration result connecting non-stabilizerness and entanglement via Fannes' inequality. Our findings provide new insights into the geometric structure of non-stabilizerness and its role in small-scale quantum systems, offering a deeper understanding of the interplay between quantum resources
Keywords
Cite
@article{arxiv.2504.12518,
title = {A trace distance-based geometric analysis of the stabilizer polytope for few-qubit systems},
author = {Alberto B. P. Junior and Santiago Zamora and Rafael A. Macêdo and Tailan S. Sarubi and Joab M. Varela and Gabriel W. C. Rocha and Darlan A. Moreira and Rafael Chaves},
journal= {arXiv preprint arXiv:2504.12518},
year = {2026}
}
Comments
20 pages, 11 figures