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arXiv · 2504.12518

A trace distance-based geometric analysis of the stabilizer polytope for few-qubit systems

Alberto B. P. Junior·Santiago Zamora·Rafael A. Macêdo·Tailan S. Sarubi·Joab M. Varela·Gabriel W. C. Rocha·Darlan A. Moreira·Rafael Chaves
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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

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Alberto B. P. Junior, Santiago Zamora, Rafael A. Macêdo, Tailan S. Sarubi, Joab M. Varela, Gabriel W. C. Rocha, Darlan A. Moreira, Rafael Chaves. 2025-04-16. A trace distance-based geometric analysis of the stabilizer polytope for few-qubit systems. https://doi.org/10.1016/j.physleta.2026.131417

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