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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.12518 |
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| _version_ | 1866910188857982976 |
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| author | Junior, Alberto B. P. Zamora, Santiago Macêdo, Rafael A. Sarubi, Tailan S. Varela, Joab M. Rocha, Gabriel W. C. Moreira, Darlan A. Chaves, Rafael |
| author_facet | Junior, Alberto B. P. Zamora, Santiago Macêdo, Rafael A. Sarubi, Tailan S. Varela, Joab M. Rocha, Gabriel W. C. Moreira, Darlan A. Chaves, Rafael |
| contents | 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 |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12518 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A trace distance-based geometric analysis of the stabilizer polytope for few-qubit systems Junior, Alberto B. P. Zamora, Santiago Macêdo, Rafael A. Sarubi, Tailan S. Varela, Joab M. Rocha, Gabriel W. C. Moreira, Darlan A. Chaves, Rafael Quantum Physics 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 |
| title | A trace distance-based geometric analysis of the stabilizer polytope for few-qubit systems |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2504.12518 |