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arXiv · 2603.13442

Non-existence of stabilizer absolutely maximally entangled states across infinitely many configurations

Hyunho Cha
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Abstract

We prove a general reduction theorem for stabilizer absolutely maximally entangled states in composite local dimension. If a stabilizer $\mathrm{AME}(n,D)$ state exists and $D=\prod_{i=1}^m q_i$ is the prime-power factorization of $D$, then for every nonempty subset of factors there exists a stabilizer $\mathrm{AME}\bigl(n,\prod_{i\in M} q_i\bigr)$ state. Thus any obstruction at a prime-power factor immediately obstructs stabilizer AME states in the composite dimension.

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Hyunho Cha. 2026-03-13. Non-existence of stabilizer absolutely maximally entangled states across infinitely many configurations. https://arxiv.org/abs/2603.13442

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