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arXiv:2007.13126 · Physical Review A

Verification of graph states in an untrusted network

Anupama Unnikrishnan, Damian Markham

Published May 13, 2022• 15 citations
arXivHTMLPDF

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.

DOI
10.1103/physreva.105.052420

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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.
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Multipartite entangled states are a fundamental resource for a wide range of quantum information processing tasks. In particular, in quantum networks, it is essential for the parties involved to be able to verify if entanglement is present before they carry out a given distributed task. Here we design and experimentally demonstrate a protocol that allows any party in a network to check if a source is distributing a genuinely multipartite entangled state, even in the presence of untrusted parties. The protocol remains secure against dishonest behaviour of the source and other parties, including the use of system imperfections to their advantage. We demonstrate the verification protocol in a three- and four-party setting using polarization-entangled photons, highlighting its potential for realistic photonic quantum communication and networking applications.
Abstract Verifying quantum states is central to certifying the correct operation of various quantum information processing tasks. In particular, in measurement-based quantum computing, checking whether correct graph states are generated is essential for reliable quantum computing. Several verification protocols for graph states have been proposed, but none of these are particularly resource efficient: multiple copies are required to extract a single state that is guaranteed to be close to the ideal one. The best protocol currently known requires O(n15) copies of the state, where n is the size of the graph state. In this paper, we construct a significantly more resource-efficient verification protocol for graph states that only requires O(n5 log n) copies. The key idea is to employ Serfling’s bound, which is a probability inequality in classical statistics. Utilizing Serfling’s bound also enables us to generalize our protocol for qudit and continuous-variable graph states. Constructing a resource-efficient verification protocol for them is non-trivial. For example, the previous verification protocols for qubit graph states that use the quantum de Finetti theorem cannot be generalized to qudit and continuous-variable graph states without tremendously increasing the resource overhead. This is because the overhead caused by the quantum de Finetti theorem depends on the local dimension. On the other hand, in our protocol, the resource overhead is independent of the local dimension, and therefore generalizing to qudit or continuous-variable graph states does not increase the overhead. The flexibility of Serfling’s bound also makes our protocol robust: our protocol accepts slightly noisy but still useful graph states.
Abstract Graph states are resource states for measurement‐based quantum computation. Verification of graph states aims to certify whether a quantum state prepared by an untrusted device is close to an ideal graph state or not. Existing verification methods have not considered verifying graph states under an adversarial scenario and noisy measurements. In this paper, a robust verification method for graph states is proposed to overcome this issue. First, a verification model for graph states is designed. Then, two types of verification protocols based on this model are proposed. In addition, the completeness and soundness of the verification protocols are calculated when the measurement devices are affected by noises. Afterward, the measurement strategy of the robust verification protocols is extended from the specific case to the general case. In order to obtain the soundness that scales as , the verification method only requires copies of the graph state, where is the size of the graph state. Finally, several numerical examples are presented to demonstrate the effect of noises on the completeness and soundness of the verification protocols.