Asymptotic survival of genuine multipartite entanglement in noisy quantum networks depends on the topology

TL;DR

This paper investigates how the topology of quantum networks influences the persistence of genuine multipartite entanglement under noise, revealing that network connectivity critically determines entanglement robustness in realistic noisy conditions.

Contribution

It introduces PEN states as a simple model for multipartite entanglement in networks and demonstrates how network topology affects entanglement robustness against noise.

Findings

Network connectivity determines entanglement robustness in noisy networks.

Genuine multipartite entanglement can be completely washed out in large networks with insufficient connectivity.

Superactivation of multipartite nonlocality is demonstrated for any number of parties.

Abstract

The study of entanglement in multipartite quantum states plays a major role in quantum information theory and genuine multipartite entanglement signals one of its strongest forms for applications. However, its characterization for general (mixed) states is a highly nontrivial problem. We introduce a particularly simple subclass of multipartite states, which we term pair-entangled network (PEN) states, as those that can be created by distributing exclusively bipartite entanglement in a connected network. We show that genuine multipartite entanglement in a PEN state depends on both the level of noise and the network topology and, in sharp contrast to the case of pure states, it is not guaranteed by the mere distribution of mixed bipartite entangled states. Our main result is a markedly drastic feature of this phenomenon: the amount of connectivity in the network determines whether genuine multipartite entanglement is robust to noise for any system size or whether it is completely washed out under the slightest form of noise for a sufficiently large number of parties. This latter case implies fundamental limitations for the application of certain networks in realistic scenarios, where the presence of some form of noise is unavoidable. To illustrate the applicability of PEN states to study the complex phenomenology behind multipartite entanglement, we also use them to prove superactivation of genuine multipartite nonlocality for any number of parties.