Rates of multi-partite entanglement transformations and applications in quantum networks

TL;DR

This paper advances the understanding of multi-partite entanglement transformations by deriving bounds on achievable rates, crucial for quantum network applications like secret sharing and quantum internet.

Contribution

It provides simple bounds on multi-partite entanglement transformation rates, identifying cases with exact rates, thus extending bipartite entanglement theory to complex quantum networks.

Findings

Derived bounds on asymptotic multi-partite entanglement transformation rates

Identified cases where bounds coincide for exact rate determination

Bound resource state distillation rates for quantum secret sharing

Abstract

The theory of the asymptotic manipulation of pure bipartite quantum systems can be considered completely understood: The rates at which bipartite entangled states can be asymptotically transformed into each other are fully determined by a single number each, the respective entanglement entropy. In the multi-partite setting, similar questions of the optimally achievable rates of transforming one pure state into another are notoriously open. This seems particularly unfortunate in the light of the revived interest in such questions due to the perspective of experimentally realizing multi-partite quantum networks. In this work, we report substantial progress by deriving surprisingly simple upper and lower bounds on the rates that can be achieved in asymptotic multi-partite entanglement transformations. These bounds are based on ideas of entanglement combing and state merging. We identify cases where the bounds coincide and hence provide the exact rates. As an example, we bound rates at which resource states for the cryptographic scheme of quantum secret sharing can be distilled from arbitrary pure tripartite quantum states, providing further scope for quantum internet applications beyond point-to-point.