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QI: Fachverband Quanteninformation

QI 20: Quantum Networks (joint session QI/Q)

QI 20.6: Vortrag

Mittwoch, 12. März 2025, 16:00–16:15, HS VIII

Genuine networks bounds on distillable GHZ and conference key in pair-entangled networks — •Anton Trushechkin, Hermann Kampermann, and Dagmar Bruß — Heinrich Heine University Düsseldorf, Faculty of Mathematics and Natural Sciences, Institute for Theoretical Physics III, Universitätsstr. 1, Düsseldorf 40225

A fundamental problem of the bipartite entanglement theory is the derivation of upper bounds on distillable entanglement (EPR pairs) and distillable secret key if a source of bipartite (entangled) states is given and LOCC (local operations and classical communication) or LOPC (local operations and public communication) maps are allowed. The same fundamental problems arises in the network scenario. We consider networks where nodes are connected with bipartite entangled sources.

Obviously, GHZ or conference key distillation is not easier than EPR or bipartite secret key distillation between two subsets of nodes constituting an arbitrary bipartition of nodes. Thus, we can apply known bipartite bounds. The existing network bounds are based on this idea of bipartition.

In the present talk, we propose genuine network bounds on distillable GHZ and conference key in pair-entangled networks, i.e. which are not reduced to bipartitions of nodes. To do this, we introduce suitable LOCC and LOPC monotones originating from putting together ideas from classical and quantum information theory and graph theory.

Keywords: quantum networks; entanglement; GHZ distillation; conference key distillation; network entanglement monotones