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

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...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2018-04, Vol.51 (17), p.175301
Main Authors: Huber, Felix, Eltschka, Christopher, Siewert, Jens, Gühne, Otfried
Format: Article
Language:English
Subjects:
absolutely maximally entangled states
multipartite entanglement
quantum error correcting codes
quantum weight enumerators
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Summary: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 2×3×3×3 system that shows maximal entanglement across every bipartition.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/aaade5