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arXiv · 2602.08410

The Finite Geometry of Breaking Quantum Secrets

Péter Lévay·Metod Saniga
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Abstract

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.

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Péter Lévay, Metod Saniga. 2026-02-09. The Finite Geometry of Breaking Quantum Secrets. https://arxiv.org/abs/2602.08410

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