Quantum network routing and local complementation

TL;DR

This paper explores how local complementation and graph state techniques can optimize quantum network routing, enabling efficient multi-party communication and reducing measurement complexity in entangled quantum networks.

Contribution

It introduces the use of local complementation in graph states to improve quantum network routing and demonstrates polynomial algorithms for structured resource classes.

Findings

Local complementation reduces measurement requirements in quantum networks.

Graph state methods enable parallel communication in bottleneck scenarios.

Polynomial algorithms exist for specific structured quantum resources.

Abstract

Quantum communication between distant parties is based on suitable instances of shared entanglement. For efficiency reasons, in an anticipated quantum network beyond point-to-point communication, it is preferable that many parties can communicate simultaneously over the underlying infrastructure; however, bottlenecks in the network may cause delays. Sharing of multi-partite entangled states between parties offers a solution, allowing for parallel quantum communication. Specifically for the two-pair problem, the butterfly network provides the first instance of such an advantage in a bottleneck scenario. The underlying method differs from standard repeater network approaches in that it uses a graph state instead of maximally entangled pairs to achieve long-distance simultaneous communication. We will demonstrate how graph theoretic tools, and specifically local complementation, help decrease the number of required measurements compared to usual methods applied in repeater schemes. We will examine other examples of network architectures, where deploying local complementation techniques provides an advantage. We will finally consider the problem of extracting graph states for quantum communication via local Clifford operations and Pauli measurements, and discuss that while the general problem is known to be NP-complete, interestingly, for specific classes of structured resources, polynomial time algorithms can be identified.