发表机构
Jagiellonian University; Polish Academy of Sciences（雅盖隆大学; 波兰科学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对每个奇素数幂维度 q，构造了稳定子 AME(2q,q) 态及其单方投影 AME(2q-1,q) 态，利用带边循环矩阵生成 MDS 码，并给出额外构造和显式矩阵。
AI 中文摘要
绝对最大纠缠（AME）态代表多体纠缠的一种极端形式：每个包含至多一半方的约化系统都是最大混合态。这些态提供完美张量和最优量子纠错码，然而其存在性仅在受限参数范围内已知。对于每个奇素数幂 $q=p^e\ge3$，我们构造一个稳定子 $\u200b\u200b\mathrm{AME}(2q,q)$ 态，其归一化单方投影产生一个稳定子 $\mathrm{AME}(2q-1,q)$ 态。一个在 $\mathbb{F}_{q^2}$ 上的闭式 $q\times q$ 带边循环矩阵 $A_q$ 生成一个 Hermitian 自对偶最大距离可分（MDS）码 $[2q,q,q+1]_{q^2}$，该码位于扩展 Reed-Solomon 类之外。在合适的基下，振幅张量定义阶为 $q^q$ 的归一化 $q$-酉复 Hadamard 矩阵，其相位为 $p$ 次根。额外的构造通过显式重缩放选定的子矩阵，产生 $\mathrm{AME}(q+3,q)$ 态以及中间粒子数下的态族。我们还提供九个显式母矩阵及相应的单方投影。
英文摘要
Absolutely maximally entangled (AME) states represent an extreme form of multipartite entanglement: every reduced system containing at most half of the parties is maximally mixed. These states provide perfect tensors and optimal quantum error-correcting codes, yet their existence is known only in restricted parameter regimes. For every odd prime power $q=p^e\ge3$, we construct a stabilizer $\mathrm{AME}(2q,q)$ state whose normalized one-party projection yields a stabilizer $\mathrm{AME}(2q-1,q)$ state. A closed-form $q\times q$ bordered-circulant matrix $A_q$ over $\mathbb{F}_{q^2}$ generates a Hermitian self-dual maximum distance separable (MDS) code $[2q,q,q+1]_{q^2}$, which lies outside the extended Reed-Solomon classes. In suitable bases, the amplitude tensors define normalized $q$-unitary complex Hadamard matrices of order $q^q$ with $p$th-root phases. Additional constructions yield $\mathrm{AME}(q+3,q)$ states and families at intermediate particle numbers through explicit rescalings of selected submatrices. We also provide nine explicit parent matrices and the corresponding one-party projections.
Comments24 pages, 1 figure. Supplemental Material included
