Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity
Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity
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DOI：
10.1088/1751-8121/aaade5
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发表时间：
2018-04-27
影响因子：
2.1
通讯作者：
Guehne, Otfried
中科院分区：
文献类型：
--
作者：
Huber, Felix;Eltschka, Christopher;Guehne, Otfried
一个纯的多体量子态称为绝对最大纠缠态（AME），如果通过追踪至少一半的粒子而得到的所有约化都是最大混合的。最大纠缠存在于每一个二分区中。在许多情况下，这些国家的存在并不清楚。借助量子纠错中的权重计数器机制和影子不等式，我们得到了大于2维的AME态存在的新界。为了完成对重量计数器机器的处理，量子MacWilliams恒等式在Bloch表示中被导出。最后，我们考虑AME状态的子系统具有不同的局部尺寸，并提出了一个例子，为2 × 3 × 3 × 3系统，显示最大纠缠在每个bipartition。
A pure multipartite quantum state is called absolutely maximally entangled (AME), if all reductions obtained by tracing out at least half of its parties are maximally mixed. Maximal entanglement is then present across every bipartition. The existence of such states is in many cases unclear. With the help of the weight enumerator machinery known from quantum error correction and the shadow inequalities, we obtain new bounds on the existence of AME states in dimensions larger than two. To complete the treatment on the weight enumerator machinery, the quantum MacWilliams identity is derived in the Bloch representation. Finally, we consider AME states whose subsystems have different local dimensions, and present an example for a 2 x 3 x 3 x 3 system that shows maximal entanglement across every bipartition.