Entanglement summoning from entanglement sharing

TL;DR

This paper characterizes the conditions under which entanglement summoning can be successfully performed in distributed quantum networks with various communication constraints, advancing understanding of entanglement management.

Contribution

It provides necessary and sufficient conditions for entanglement summoning with bidirected causal connections and sufficient conditions for the general case, building on recent entanglement sharing schemes.

Findings

Established an if and only if condition for bidirected causal connections.

Provided sufficient conditions for tasks with mixed causal connections.

Extended the theoretical framework for entanglement summoning in constrained networks.

Abstract

In an entanglement summoning task, a set of distributed, co-operating parties attempt to fulfill requests to prepare entanglement between distant locations. The parties share limited communication resources: timing constraints may require the entangled state be prepared before some pairs of distant parties can communicate, and a restricted set of links in a quantum network may further constrain communication. Building on earlier work, we continue the characterization of entanglement summoning. We give an if and only if condition on entanglement summoning tasks with only bidirected causal connections, and provide a set of sufficient conditions addressing the most general case containing both oriented and bidirected causal connections. Our results rely on the recent development of entanglement sharing schemes.