Renormalising entanglement distillation

TL;DR

This paper introduces a new framework for entanglement distillation that accounts for correlations from memory channels, using renormalisation techniques from condensed matter physics to ensure convergence to maximally entangled states.

Contribution

It combines ideas from condensed-matter physics, quantum error correction, and Markov processes to analyze entanglement distillation with correlated initial states.

Findings

Proves convergence to maximally entangled states under certain conditions

Identifies parameter regions where the renormalisation flow reaches fixed points

Extends entanglement distillation theory to correlated, non-i.i.d. scenarios

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 realise quantum key distribution schemes. Usually, it is assumed that the initial entangled pairs are i.i.d. 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 renormalisation 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 prove convergence to maximally entangled states, arising as the fixed points of a matrix-product operator renormalisation flow.