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Quantum 2.0 Conference and Exhibition

Experimental Device-Independent Certification of a 4-qubit GHZ State

Laura dos Santos Martins, Nicolas Laurent-Puig, Ivan Šupić, Damian Markham, Eleni Diamanti

Published Jan 1, 2025• 0 citations
Publisher

Abstract

Authentication of quantum resources is crucial for quantum protocols. We adopt Gocanin et al. [3] protocol to experimentally certify a four-photon GHZ state in a device-independent framework, without assuming identically and independently distributed states. This certification is performed using our compact, high-fidelity entangled photon source.

DOI
10.1364/quantum.2025.qm3b.4

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Authentication of quantum resources is crucial for quantum protocols. We adopt Gocanin et al. [3] protocol to experimentally certify a four-photon GHZ state in a device-independent framework, without assuming identically and independently distributed states. This certification is performed using our compact, high-fidelity entangled photon source.
The certification of quantum resources is a critical tool in the development of quantum information processing. In particular, quantum state verification is a fundamental building block for communication and computation applications, determining whether the involved parties can trust the resources at hand or whether the application should be aborted. Self-testing methods have been used to tackle such verification tasks in a device-independent (DI) setting. However, these approaches commonly consider the limit of large (asymptotic), independent and identically distributed (IID) samples, which weakens the DI claim and poses serious challenges to their experimental implementation. Here, we overcome these challenges by adopting a theoretical protocol, enabling the certification of quantum states in the few-copies and non-IID regime and by leveraging a high-fidelity multipartite entangled photon source. This allows us to show the efficient and DI certification of a single copy of a four-qubit GHZ state that can readily be used for the robust and reliable implementation of quantum information tasks.
The certification of quantum resources is a critical tool in the development of quantum information processing. In particular, quantum state verification is a fundamental building block for communication and computation applications, determining whether the involved parties can trust the resources at hand or whether the application should be aborted. Self-testing methods have been used to tackle such verification tasks in a device-independent (DI) setting. However, these approaches commonly consider the limit of large (asymptotic), independent and identically distributed (IID) samples, which weakens the DI claim and poses serious challenges to their experimental implementation. Here, we overcome these challenges by adopting a theoretical protocol, enabling the certification of quantum states in the few-copies and non-IID regime and by leveraging a high-fidelity multipartite entangled photon source. This allows us to show the efficient and DI certification of a single copy of a four-qubit GHZ state that can readily be used for the robust and reliable implementation of quantum information tasks.
Standard quantum verification and certification protocols often assume that experimental sources emit independent and identically distributed (i.i.d.) states. In realistic scenarios, however, temporal drift, memory effects, feedback, and correlated noise can violate this assumption, causing standard analyses to underestimate uncertainty and overestimate device performance. Here, we introduce a general framework for quantum verification and certification in which the state produced in each round may depend arbitrarily on the preceding experimental history. Our method provides rigorous confidence intervals for observable expectation values averaged over the experimental trajectory. The framework covers both full verification, in which every state is measured, and spot-checking certification, in which a randomly selected subset is tested to certify the average observable value of the complementary, remaining systems. We apply the framework to importance-sampled Pauli measurements for direct fidelity estimation, energy estimation, and entanglement witnessing, and to classical shadows, allowing multiple observables to be certified simultaneously from the same test data. We illustrate the framework numerically and demonstrate it experimentally through Bell-state certification on a quantum processor.
Entangled quantum states are essential ingredients for many quantum technologies, but they must be validated before they are used. As a full characterization is prohibitively resource intensive, recent work has focused on developing methods to efficiently extract a few parameters of interest, in a so-called verification framework. Most existing approaches are based on preparing an ensemble of nominally identical and independently distributed (IID) quantum states and then measuring each copy of the ensemble. However, this leaves no states left for the intended quantum tasks and the IID assumptions do not always hold experimentally. To overcome these challenges, we experimentally implement quantum state certification (QSC), which measures only a subset of the ensemble, certifying the fidelity of multiple copies of the remaining states. We use active optical switches to randomly sample from sources of two-photon Bell states and three-photon GHZ (Greenberger-Horn-Zeilinger) states, reporting statistically sound fidelities in real time without destroying the entire ensemble. In addition, our QSC protocol removes the assumption that the states are identically distributed (but still assumes independent copies); can achieve close N −1 scaling, in the number of states measured N ; and can be implemented in a device-independent manner. Together, these benefits make our QSC protocol suitable for benchmarking large-scale quantum computing devices and deployed quantum communication setups relying on entanglement in both standard and adversarial situations.
Authentication of quantum sources is a crucial task in building reliable and efficient protocols for quantum-information processing.Steady progress vis-à-vis verification of quantum devices in the scenario with fully characterized measurement devices has been observed in recent years.When it comes to the scenario with uncharacterized measurements, the so-called black-box scenario, practical verification methods are still rather scarce.Development of self-testing methods is an important step forward, but these results so far have been used for reliable verification only by considering the asymptotic behavior of large, identically and independently distributed (IID) samples of a quantum resource.Such strong assumptions deprive the verification procedure of its truly device-independent character.In this paper, we develop a systematic approach to device-independent verification of quantum states free of IID assumptions in the finite copy regime.Remarkably, we show that device-independent verification can be performed with optimal sample efficiency.Finally, for the case of independent copies, we develop a device-independent protocol for quantum state certification: a protocol in which a fragment of the resource copies is measured to warrant the rest of the copies to be close to some target state.