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.
Dimers on surface graphs and spin structures. I
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abstract
Partition functions for dimers on closed oriented surfaces are known to be alternating sums of Pfaffians of Kasteleyn matrices. In this paper, we obtain the formula for the coefficients in terms of discrete spin structures.
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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.