Quantum Lunch: Renormalising entanglement distillation

Speaker: Earl Campbell

Title: Renormalising 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, 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 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 - that of renormalization and of 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 rigorously prove convergence to maximally entangled states, arising as the fixed points of a matrix-product operator renormalization flow.