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QI: Fachverband Quanteninformation
QI 21: Quantum Information: Concepts and Methods III
QI 21.4: Vortrag
Freitag, 13. März 2026, 10:30–10:45, BEY/0245
Characterizing genuine multipartite high-dimensional entanglement with the partition rank — •Sophia Denker1, Ismaël Septembre1, Robin Krebs2, and Otfried Gühne1 — 1Universität Siegen, Siegen, Germany — 2Technische Universität Darmstadt, Darmstadt, Germany
Entanglement is an important resource in quantum information as it has been demonstrated to bring advantages in several applications. In fact, these advantages are even higher when going to larger systems, i. e. increasing the number of particles or their local dimensions. However, with increasing system size also the characterization and quantification of quantum entanglement becomes more complex.
We introduce a new measure for the entanglement dimensionality of multiparticle states, based on the partition rank. The partition rank is given by the number of biseparable terms, needed to decompose a multipartite quantum state. Different from the Schmidt decomposition the terms appearing here are allowed to be separable with respect to different bipartitions, making this approach a truly multipartite quantification. We translate the problem of finding the closest state with a certain partition rank to the problem of finding the closest product state, which is known as the geometric measure of entanglement. This translation allows us to tackle this new problem with well-established methods. Along the way, we identify quantum states which are maximally entangled with respect to this measure and further show that our methods could make a contribution towards solving an open problem in mathematics, related to the partition rank.
Keywords: quantum entanglement; high-dimensional entanglement; multipartite entanglement; geometric measure; partition rank