title: Renormalizing Entanglement Distillation.
abstract: Entanglement distillation refers to the task of transforming a collection of weakly entangled pairs into fewer highly entangled ones. It is a core ingredient in quantum repeater protocols, which are needed to transmit entanglement over arbitrary distances in order to realize quantum key distribution schemes. Usually, it is assumed that the initial entangled pairs are identically and independently distributed and are uncorrelated with each other, an assumption that might not be reasonable at all in any entanglement generation process involving memory channels. Here, we introduce a framework that captures entanglement distillation in the presence of natural correlations arising from memory channels. Conceptually, we bring together ideas from condensed-matter physics-ideas from renormalization and matrix-product states and operators-with those of local entanglement manipulation, Markov chain mixing, and quantum error correction. We identify meaningful parameter regions for which we prove convergence to maximally entangled states, arising as the fixed points of a matrix-product operator renormalization flow.
authors.affiliation: Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany.
authors.forename: Stephan
authors.initials: S
authors.lastname: Waeldchen
authors.affiliation: Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany.
authors.forename: Janina
authors.initials: J
authors.lastname: Gertis
authors.affiliation: Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom.
authors.forename: Earl T
authors.initials: ET
authors.lastname: Campbell
authors.affiliation: Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany.
authors.forename: Jens
authors.initials: J
authors.lastname: Eisert