Entanglement purity in quadratic-phase states over finite fields is exactly determined by the rank of the phase matrix, with AME states existing precisely when all bipartition submatrices have full rank.
Each cost evaluation requires computing ranks for a subset of bipartitions (only those affected by the move)
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Entanglement-Rank Duality in Quadratic Phase Quantum States
Entanglement purity in quadratic-phase states over finite fields is exactly determined by the rank of the phase matrix, with AME states existing precisely when all bipartition submatrices have full rank.