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Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity

Huber, Felix ; Eltschka, Christopher ; Siewert, Jens ; Gühne, Otfried



Abstract

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 ...

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