Verification of graph states in an untrusted network

TL;DR

This paper introduces an efficient protocol for verifying the integrity of various graph states in an untrusted network, ensuring their suitability for quantum computing and communication tasks.

Contribution

It presents a practical, scalable verification protocol applicable to a wide range of graph states, including cluster and GHZ states, with maintained security and efficiency.

Findings

Protocol is globally efficient for many useful graph states.

Verification remains secure with increasing graph size, with some cost increase.

Protocols are practical, requiring only local measurements and classical communication.

Abstract

Graph states are a large class of multipartite entangled quantum states that form the basis of schemes for quantum computation, communication, error correction, metrology, and more. In this work, we consider verification of graph states generated by an untrusted source and shared between a network of possibly dishonest parties. This has implications in certifying the application of graph states for various distributed tasks. We present a protocol which is globally efficient for a large family of useful graph states, including cluster states, GHZ states, cycle graph states and more. For general graph states, efficiency with respect to the security parameter is maintained, though there is a cost increase with the size of the graph state. The protocols are practical, requiring only multiple copies of the graph state, local measurements and classical communication.