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| Autors principals: | , |
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| Format: | Preprint |
| Publicat: |
2026
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| Matèries: | |
| Accés en línia: | https://arxiv.org/abs/2602.08410 |
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| _version_ | 1866908831143952384 |
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| author | Lévay, Péter Saniga, Metod |
| author_facet | Lévay, Péter Saniga, Metod |
| contents | Using a finite geometric framework for studying the pentagon and heptagon codes we show that the concepts of quantum secret sharing and contextuality can be studied in a nice and unified manner. The basic idea is a careful study of the respective $2+3$ and $3+4$ tensorial factorizations of the elements of the stabilizer groups of these codes. It is demonstrated in detail how finite geometric structures entailing a specific three-qubit (resp. four-qubit) embedding of binary symplectic polar spaces of rank two (resp. three), corresponding to these factorizations, govern issues of contextuality and entanglement needed for a geometric understanding of quantum secret sharing. Using these results for the $(3,5)$ and $(4,7)$ threshold schemes explicit secret breaking protocols are derived. Our results hint at a novel geometric way of looking at contextual configurations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08410 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Finite Geometry of Breaking Quantum Secrets Lévay, Péter Saniga, Metod Quantum Physics Using a finite geometric framework for studying the pentagon and heptagon codes we show that the concepts of quantum secret sharing and contextuality can be studied in a nice and unified manner. The basic idea is a careful study of the respective $2+3$ and $3+4$ tensorial factorizations of the elements of the stabilizer groups of these codes. It is demonstrated in detail how finite geometric structures entailing a specific three-qubit (resp. four-qubit) embedding of binary symplectic polar spaces of rank two (resp. three), corresponding to these factorizations, govern issues of contextuality and entanglement needed for a geometric understanding of quantum secret sharing. Using these results for the $(3,5)$ and $(4,7)$ threshold schemes explicit secret breaking protocols are derived. Our results hint at a novel geometric way of looking at contextual configurations. |
| title | The Finite Geometry of Breaking Quantum Secrets |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2602.08410 |