SAMOP 2021 – scientific programme

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QI: Fachverband Quanteninformation

QI 13: Quantum Information and Foundations II

QI 13.2: Talk

Friday, September 24, 2021, 11:00–11:15, H4

An algorithm for maximizing the geometric measure of entanglement — •Jonathan Steinberg and Otfried Gühne — Universität Siegen, Siegen, Deutschland

The characterization of multipartite entanglement is an important subject in order to make quantum advantages accessible for applications. One proper multipartite entanglement measure, i.e., a measure that does not rely on averages of bipartite entanglement, is the geometric measure. In this work we propose an algorithm which aims to find maximally entangled states with respect to the geometric measure. As it turns out, the algorithm’s update rule constitutes a gradient descent, providing fast convergences and applicability to large systems. Surprisingly, we find that the maximally entangled states for a n-partite qudit system is in the case of existence always given by an AME(n,d) state, except for n=3, where the w-state maximizes the measure. However, for those cases where AME states do not exist, we present a family of states, called maximally marginal symmetric, that maximizes the geometric measure. Further we discuss how the algorithm could be utilized to find new AME states as AME(8,4).