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arXiv:2408.01299 · Physical Review Letters

Complete Self-Testing of a System of Remote Superconducting Qubits

Simon Storz, Anatoly Kulikov, Josua Schär, Victor Barizien, Xavier Valcarce, Florence Berterottière, Nicolas Sangouard, Jean-Daniel Bancal, Andreas J. Wallraff

Published Jun 12, 2025• 10 citations
arXivHTMLPDF

Abstract

Self-testing protocols enable the certification of quantum systems in a device-independent manner, i.e., without knowledge of the inner workings of the quantum devices under test. Here, we demonstrate this high standard for characterization routines with superconducting circuits, a prime platform for building large-scale quantum computing systems. We first develop the missing theory allowing for the self-testing of Pauli measurements. We then self-test Bell pair generation and measurements at the same time, performing a complete self-test in a system composed of two entangled superconducting circuits operated at a separation of 30 m. In an experiment based on 17 million trials, we measure an average CHSH (Clauser-Horne-Shimony-Holt) S value of 2.236. Without relying on additional assumptions on the experimental setup, we certify an average Bell state fidelity of at least 58.9% and an average measurement fidelity of at least 89.5% in a device-independent manner, both with 99% confidence. This enables applications in the field of distributed quantum computing and communication with superconducting circuits, such as delegated quantum computing.

DOI
10.1103/nv7d-k3wr

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Self-testing protocols enable the certification of quantum systems in a device-independent manner, i.e., without knowledge of the inner workings of the quantum devices under test. Here, we demonstrate this high standard for characterization routines with superconducting circuits, a prime platform for building large-scale quantum computing systems. We first develop the missing theory allowing for the self-testing of Pauli measurements. We then self-test Bell pair generation and measurements at the same time, performing a complete self-test in a system composed of two entangled superconducting circuits operated at a separation of 30 m. In an experiment based on 17 million trials, we measure an average CHSH (Clauser-Horne-Shimony-Holt) S value of 2.236. Without relying on additional assumptions on the experimental setup, we certify an average Bell state fidelity of at least 58.9% and an average measurement fidelity of at least 89.5% in a device-independent manner, both with 99% confidence. This enables applications in the field of distributed quantum computing and communication with superconducting circuits, such as delegated quantum computing.
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Abstract Superposition, entanglement and non-locality constitute fundamental features of quantum physics. The fact that quantum physics does not follow the principle of local causality1–3 can be experimentally demonstrated in Bell tests4 performed on pairs of spatially separated, entangled quantum systems. Although Bell tests, which are widely regarded as a litmus test of quantum physics, have been explored using a broad range of quantum systems over the past 50 years, only relatively recently have experiments free of so-called loopholes5 succeeded. Such experiments have been performed with spins in nitrogen–vacancy centres6, optical photons7–9 and neutral atoms10. Here we demonstrate a loophole-free violation of Bell’s inequality with superconducting circuits, which are a prime contender for realizing quantum computing technology11. To evaluate a Clauser–Horne–Shimony–Holt-type Bell inequality4, we deterministically entangle a pair of qubits12 and perform fast and high-fidelity measurements13 along randomly chosen bases on the qubits connected through a cryogenic link14 spanning a distance of 30 metres. Evaluating more than 1 million experimental trials, we find an average S value of 2.0747 ± 0.0033, violating Bell’s inequality with a P value smaller than 10−108. Our work demonstrates that non-locality is a viable new resource in quantum information technology realized with superconducting circuits with potential applications in quantum communication, quantum computing and fundamental physics15.
Self-testing is a method to certify devices from the result of a Bell test. Although examples of noise tolerant self-testing are known, it is not clear how to deal efficiently with a finite number of experimental trials to certify the average quality of a device without assuming that it behaves identically at each run. As a result, existing self-testing results with finite statistics have been limited to guarantee the proper working of a device in just one of all experimental trials, thereby limiting their practical applicability. We here derive a method to certify through self-testing that a device produces states on average close to a Bell state without assumption on the actual state at each run. Thus the method is free of the I.I.D. (independent and identically distributed) assumption. Applying this new analysis on the data from a recent loophole-free Bell experiment, we demonstrate the successful distribution of Bell states over 398 meters with an average fidelity of ≥ 55.50% at a confidence level of 99%. Being based on a Bell test free of detection and locality loopholes, our certification is evidently device-independent, that is, it does not rely on trust in the devices or knowledge of how the devices work. This guarantees that our link can be integrated in a quantum network for performing long-distance quantum communications with security guarantees that are independent of the details of the actual implementation.
Self-testing provides a device-independent framework for certifying quantum properties based solely on input-output statistics while treating quantum devices as black boxes. It has evolved significantly from its origins in bipartite systems to applications in multipartite entanglement and, more recently, genuinely entangled subspaces. Notably, It has been revealed that the logical subspaces of numerous stabilizer quantum error correction codes are exclusively composed of genuinely multipartite entangled states, opening new avenues for developing device-independent tools to characterize these subspaces. In this work, we leverage the self-testing technique to certify genuinely entangled logical subspaces within the five-qubit code using both photonic and superconducting platforms. This is achieved by preparing informationally complete logical states, simulating Pauli errors on a physical qubit, and testing several stabilizer-formalized Bell inequalities. Our certification is supported by an extractability measure of at least0.828±0.006and0.621±0.007for the photonic and superconducting systems, respectively. Our results demonstrate the feasibility of device-independent certification of general entangled quantum structures in experimental settings, extending beyond quantum states and quantum measurements.
Quantum entanglement is the key resource for quantum information processing. Device-independent certification of entangled states is a long standing open question, which arouses the concept of self-testing. The central aim of self-testing is to certify the state and measurements of quantum systems without any knowledge of their inner workings, even when the used devices cannot be trusted. Specifically, utilizing Bell's theorem, it is possible to place a boundary on the singlet fidelity of entangled qubits. Here, beyond this rough estimation, we experimentally demonstrate a complete self-testing process for various pure bipartite entangled states up to four dimensions, by simply inspecting the correlations of the measurement outcomes. We show that this self-testing process can certify the exact form of entangled states with fidelities higher than 99.9% for all the investigated scenarios, which indicates the superior completeness and robustness of this method. Our work promotes self-testing as a practical tool for developing quantum techniques.
Characterizing large quantum systems with minimal assumptions is a central challenge in quantum information science. Self-testing provides the strongest form of certification by identifying the underlying quantum state solely from observed measurement statistics. However, existing self-testing methods for generic nnn-partite states face a scalability barrier, requiring exponentially many samples in the system size. In this work, we overcome this barrier by introducing a protocol that robustly self-tests almost all nnn-qubit states with only polynomial sample complexity. The key ingredient is an efficient scheme for device-independently evaluating multipartite Pauli measurements, which can be implemented using only a linear number of ancillary Bell pairs together with standard projective and Bell measurements, well within the reach of current quantum technology. Beyond self-testing states, our scheme provides a general framework for implementing a wide range of learning and certification protocols in the device-independent setting, thereby opening a scalable route to device-independent quantum information processing in large-scale quantum networks.