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arXiv:2406.03908 · Physical Review A

Noisy certification of continuous-variable graph states

Éloi Descamps, Damian Markham

Published Feb 10, 2025• 2 citations
arXivHTMLPDF

Abstract

Continuous variables (CV) offer a promising platform for the development of various applications, such as quantum communication, computing, and sensing, and CV graph states represent a family of powerful entangled resource states for all these areas. In many of these protocols, a crucial aspect is the certification of the quantum state subsequently used. While numerous protocols exist, most rely on assumptions unrealistic for physical continuous-variable states, such as infinite precision in quadrature measurement or the use of states requiring infinite squeezing. In this work, we adapt existing protocols to deal with these unavoidable considerations and use them to certify their application for different quantum information tasks. More specifically, we show how CV graph states can be efficiently verified and certified even in a noisy and imperfect setting. We then discuss how our findings impact the usability of states obtained after the protocol for different applications, including quantum teleportation, computing, and sensing.

DOI
10.1103/physreva.111.022413

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Continuous variables (CV) offer a promising platform for the development of various applications, such as quantum communication, computing, and sensing, and CV graph states represent a family of powerful entangled resource states for all these areas. In many of these protocols, a crucial aspect is the certification of the quantum state subsequently used. While numerous protocols exist, most rely on assumptions unrealistic for physical continuous-variable states, such as infinite precision in quadrature measurement or the use of states requiring infinite squeezing. In this work, we adapt existing protocols to deal with these unavoidable considerations and use them to certify their application for different quantum information tasks. More specifically, we show how CV graph states can be efficiently verified and certified even in a noisy and imperfect setting. We then discuss how our findings impact the usability of states obtained after the protocol for different applications, including quantum teleportation, computing, and sensing.
Continuous-variable quantum information, encoded into infinite-dimensional quantum systems, is a promising platform for the realization of many quantum information protocols, including quantum computation, quantum metrology, quantum cryptography, and quantum communication. To successfully demonstrate these protocols, an essential step is the certification of multimode continuous-variable quantum states and quantum devices. This problem is well studied under the assumption that multiple uses of the same device result in identical and independently distributed (i.i.d.) operations. However, in realistic scenarios, identical and independent state preparation and calls to the quantum devices cannot be generally guaranteed. Important instances include adversarial scenarios and instances of time-dependent and correlated noise. In this Letter, we propose the first set of reliable protocols for verifying multimode continuous-variable entangled states and devices in these non-i.i.d scenarios. Although not fully universal, these protocols are applicable to Gaussian quantum states, non-Gaussian hypergraph states, as well as amplification, attenuation, and purification of noisy coherent states.
Secure and reliable certification of quantum resources is a fundamental challenge in the advancement of next-generation quantum technologies, particularly as devices become more complex and integrated into practical applications, where parts of the system may be untrusted or inaccessible by users. Addressing this challenge requires certification methods that rely on minimal assumptions and limited trust while still faithfully and reliably verifying the quantum resources in question. For infinite-dimensional bosonic systems, existing certification methods rely on fully trusted and well-calibrated measurement systems, leaving significant security vulnerabilities open. In this work, we present the first experimental demonstration of measurement-device-independent (MDI) certification schemes for infinite-dimensional bosonic systems, where the certification process is conducted using entirely untrusted measurement devices and assuming only the trusted preparation of coherent states. Specifically, we implement schemes for the MDI certification of continuous-variable (CV) entanglement and the operation of an elementary optical CV quantum memory. We leverage techniques of Bayesian metrology and exploit the practicality and accessibility of Gaussian quantum optics to achieve secure and efficient certification. These results demonstrate the potential of the MDI framework to enhance trust in quantum technologies with applications in quantum communication and quantum computing.
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.
In measurement-based quantum computing (MBQC), computation is carried out by a sequence of measurements and corrections on an entangled state. Flow, and related concepts, are powerful techniques for characterising the dependence of the corrections on previous measurement results. We introduce flow-based methods for quantum computation with continuous-variable graph states, which we call CV-flow. These are inspired by, but not equivalent to, the notions of causal flow and g-flow for qubit MBQC. We also show that an MBQC with CV-flow approximates a unitary arbitrarily well in the infinite-squeezing limit, addressing issues of convergence which are unavoidable in the infinite-dimensional setting. In developing our proofs, we provide a method for converting a CV-MBQC computation into a circuit form, analogous to the circuit extraction method of Miyazaki et al, and an efficient algorithm for finding CV-flow when it exists based on the qubit version by Mhalla and Perdrix. Our results and techniques naturally extend to the cases of MBQC for quantum computation with qudits of prime local dimension.
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.