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Physical Review Letters

Reliable Quantum Steering Detection under Imperfect Measurement

Ting Zhang, Wenhao Zhang, Jing-Tao Qiu, Leilei Huang, Xiao Yuan, Qi-Ming Ding

Published Feb 4, 2026• 1 citation
Publisher

Abstract

Quantum steering, a fundamental manifestation of nonlocal quantum correlations, plays a vital role in quantum key distribution, quantum randomness generation, and quantum metrology. Reliable experimental detection of quantum steering is therefore a key task in quantum information science, but it is often hindered by measurement imperfections. Here, we introduce a randomized measurement protocol designed to mitigate the effects of imperfect measurements and enhance detection reliability. We theoretically prove that this approach effectively suppresses measurement errors by requiring only local operations on the trusted party; moreover, its dimension-independent nature ensures ready adaptability to quantum systems of arbitrary finite size. We experimentally validate the method using polarization-entangled photons, demonstrating consistent performance under controlled misalignments for both 2- and 3-setting configurations. Our results provide a practical and reliable framework for steering detection in realistic experimental conditions, paving the way for its integration into quantum certification and communication protocols.

DOI
10.1103/wgqg-hfw8

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Quantum steering, a fundamental manifestation of nonlocal quantum correlations, plays a vital role in quantum key distribution, quantum randomness generation, and quantum metrology. Reliable experimental detection of quantum steering is therefore a key task in quantum information science, but it is often hindered by measurement imperfections. Here, we introduce a randomized measurement protocol designed to mitigate the effects of imperfect measurements and enhance detection reliability. We theoretically prove that this approach effectively suppresses measurement errors by requiring only local operations on the trusted party; moreover, its dimension-independent nature ensures ready adaptability to quantum systems of arbitrary finite size. We experimentally validate the method using polarization-entangled photons, demonstrating consistent performance under controlled misalignments for both 2- and 3-setting configurations. Our results provide a practical and reliable framework for steering detection in realistic experimental conditions, paving the way for its integration into quantum certification and communication protocols.
Quantum steering, as a manifestation of nonlocal quantum correlations, plays a crucial role in enabling various quantum information processing tasks. However, practical implementations are often hindered by significant challenges arising from imperfect or untrusted measurement devices. This study investigates the impact of measurement inaccuracies on quantum steering, with a particular focus on errors in the untrusted party's measurement devices. We first analyze how such errors affect the evaluation of steering inequalities, and then derive bipartite steering inequalities based on correlation matrices under imperfect measurements. Our findings show that even small measurement errors can significantly compromise the certification of quantum steerability, an effect that becomes particularly pronounced as the system dimension increases. Furthermore, by extending the proposed steering inequality to a modified tripartite scenario via correlation matrices, we demonstrate that the influence of measurement imperfections is far more severe in multipartite quantum steering than in the bipartite case. Our results underscore the critical need to account for measurement imperfections in experimental quantum steering and provide a theoretical framework for characterizing and mitigating these effects in high-dimensional quantum systems.
We consider quantum steering certification in multipartite networks, with a focus on minimal trust scenarios: all-except-one parties are untrusted and treated device-independently. We show that it is always possible to lift steering certification to the measurement-device-independent regime, in which even the (last) trusted party can treat their local hardware as a black-box, except for a set of fiduciary quantum states used as the inputs to the experiment. This holds both for finite-dimensional systems as well as for bosonic continuous-variable systems, which we characterize in terms of semi-quantum games in the bipartite case. Additionally, we introduce measurement-device-independent network steering protocols based entirely on Gaussian operations -- which cannot be used for fully device-independent protocols, and thus become instead a viable option for minimal trust certification as soon as a single trusted input is inserted in the network. Our results present a basis for steering-based applications (such as randomness generation) with minimal trust beyond full nonlocality and with feasible experimental requirements.
Bell non-locality between distant quantum systems—that is, joint correlations which violate a Bell inequality—can be verified without trusting the measurement devices used, nor those performing the measurements. This leads to unconditionally secure protocols for quantum information tasks such as cryptographic key distribution. However, complete verification of Bell non-locality requires high detection efficiencies, and is not robust to typical transmission losses over long distances. In contrast, quantum or Einstein–Podolsky–Rosen steering, a weaker form of quantum correlation, can be verified for arbitrarily low detection efficiencies and high losses. The cost is that current steering-verification protocols require complete trust in one of the measurement devices and its operator, allowing only one-sided secure key distribution. Here we present measurement-device-independent steering protocols that remove this need for trust, even when Bell non-locality is not present. We experimentally demonstrate this principle for singlet states and states that do not violate a Bell inequality. Quantum steering is a form of quantum non-locality that can be verified for arbitrarily low detection efficiencies and high losses at the price of requiring complete trust in one of the parties. Here, Kocsis et al. present measurement-device-independent steering protocols that remove this need for trust.
Quantum steering is a fundamental quantum correlation that plays a pivotal role in quantum technologies, but its verification crucially relies on precise measurements -- an assumption often undermined by practical imperfections. Here, we investigate multipartite steering verification under imprecise measurements and develop a quantitative method that effectively eliminates false positives induced by measurement imprecision. A comparison with a device-independent approach demonstrates that our method accurately delineates the scope of valid verification. In a special case, our method also enables the verification of multipartite entanglement under nonideal conditions. These results substantially enhance the robustness of multipartite steering and entanglement verification against measurement imprecision, thereby promoting their applicability in realistic quantum technologies.
We analyze and experimentally demonstrate quantum steering using criteria based on generalized entropies and criteria with minimal assumptions based on the so-called dimension-bounded steering. Further, we investigate and compare their robustness against experimental imperfections such as misalignment in the shared measurement reference frame. While entropy based criteria are robust against imperfections in state preparation, we demonstrate an advantage in dimension-bounded steering in the presence of measurement imprecision. As steering with such minimal assumptions is easier to reach than fully nonlocal correlations, and as our setting requires very little trust in the measurement devices, the results provide a candidate for the costly Bell tests while remaining highly device independent.
In a measurement-device-independent or quantum-refereed protocol, a referee can verify whether two parties share entanglement or Einstein-Podolsky-Rosen (EPR) steering without the need to trust either of the parties or their devices. The need for trusting a party is substituted by a quantum channel between the referee and that party, through which the referee encodes the measurements to be performed on that party's subsystem in a set of nonorthogonal quantum states. In this Letter, an EPR-steering inequality is adapted as a quantum-refereed EPR-steering witness, and the trust-free experimental verification of higher dimensional quantum steering is reported via preparing a class of entangled photonic qutrits. Further, with two measurement settings, we extract 1.106±0.023 bits of private randomness per every photon pair from our observed data, which surpasses the one-bit limit for projective measurements performed on qubit systems. Our results advance research on quantum information processing tasks beyond qubits.