Distillation of multipartite entangled states for arbitrary subsets of parties in noisy quantum networks of increasing size

TL;DR

This paper investigates the potential to extract pure entangled states from noisy quantum networks for specific subsets of parties, establishing conditions under which partial distillation is feasible despite noise.

Contribution

It introduces the problem of partial distillability in noisy quantum networks and provides necessary and sufficient conditions based on network connectivity parameters.

Findings

Multipartite distillation is obstructed by constant noise levels.

Partial distillability is achievable with sufficient network connectivity growth.

Explicit network constructions demonstrate partial distillability with slow connectivity growth.

Abstract

Quantum network states are multipartite states built from distributing pairwise entanglement among parties and underpin the paradigm of quantum networks for quantum information processing. In this work we introduce the problem of partial distillability in noisy quantum networks. This corresponds to the possibility of distilling by local operations and classical communication an arbitrary pure state for an arbitrary subset of parties starting from a single copy of a quantum network state of an increasing number of parties that share noisy (i.e. mixed) bipartite entangled states. Here, distillation means that the target state is obtained with fidelity as close to 1 as desired as the size of the network increases when the pairwise entangled links support a constant amount of noise. While we prove an obstruction to multipartite distillation protocols after teleportation with channels with constant noise, we show that partial distillability is indeed possible if certain well-established graph-theoretic parameters that measure the connectivity in the network grow fast enough with its size. We give necessary as well as sufficient conditions for partial distillability in terms of these parameters and we moreover provide explicit constructions of networks with partial distillability and a relatively slow connectivity growth.