Scalable Certification of Entanglement in Quantum Networks

TL;DR

This paper introduces scalable, efficient methods for certifying genuine multipartite entanglement in quantum networks, overcoming limitations of previous techniques by using sub-symmetric witnesses that are practical for large systems.

Contribution

The authors develop a family of sub-symmetric witnesses linked to graph theory, enabling scalable and resource-efficient entanglement certification in quantum networks.

Findings

SSWs are analytically connected to graph cut spaces.

Optimal detection reduces to a linear program, increasing efficiency.

SSWs require local measurements with resource demands independent of network size.

Abstract

Quantum networks form the backbone of long-distance quantum information processing. Genuine multipartite entanglement (GME) serves as a key indicator of network performance and overall state quality. However, the widely used methods for certifying GME suffer from a major drawback that they either detect only a limited range of states or are applicable only to systems with a small number of parties. To overcome these limitations, we propose a family of sub-symmetric witnesses (SSWs), which are tractable both theoretically and experimentally. Analytically, we establish a connection between SSWs and the cut space of graph theory, enabling several powerful detection criteria tailored to practical quantum networks. Numerically, we show that the optimal detection can be formulated as a linear program, offering a significant efficiency advantage over the semidefinite programs commonly employed in quantum certification. Experimentally, SSWs can be evaluated via local measurements, with resource requirements independent of the local dimension in general, and even independent of the overall network size in many practical networks.