Graph-state inner products are governed by the F2-rank of the adjacency matrix and the Arf invariant, yielding a nonlocal Bell-pair factorization of the Hilbert space.
Yoshida,Recovery algorithms for Clifford Hayden-Preskill problem,2106.15628
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Fun with Graph States: Nonlocal Bell Pairs and the Arf Invariant
Graph-state inner products are governed by the F2-rank of the adjacency matrix and the Arf invariant, yielding a nonlocal Bell-pair factorization of the Hilbert space.