Erlangen 2018 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 68: Quantum Information (Concepts and Methods) V
Q 68.1: Talk
Friday, March 9, 2018, 10:30–10:45, K 1.019
Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity — •Felix Huber1, Christopher Eltschka2, Jens Siewert3, and Otfried Gühne1 — 1Naturwissenschaftlich-Technische Fakultät, Universität Siegen, D-57068 Siegen, Germany — 2Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany — 3Departamento de Quimica Fisica, Universidad del Pais Vasco UPV/EHU, E-48080 Bilbao, Spain
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 generalized 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 2x3x3x3 system that shows maximal entanglement across every bipartition.