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arXiv:2606.13667

Semi-Device-Independent Certification for Nonlocality without Entanglement

Hanwool Lee, Joonwoo Bae

quant-phSubmitted Jun 11, 2026• Announced Jun 12, 2026• 0 citations• Revised Jun 15, 2026 (v2)
v1 · Jun 11, 2026v2 · Jun 15, 2026
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Abstract

In this work, we present the framework for demonstrating and certifying the distinction between measurements in an entangled basis, called global measurements, and local operations and classical communication (LOCC), known as nonlocality without entanglement (NLWE). To be precise, we show NLWE via a maximum-confidence measurement in terms of a guess per detection event, called a confidence, a fine-grained guessing probability that encompasses both minimum-error and unambiguous state-discrimination strategies. We show that NLWE for unknown measurements can be certified, given the measurement-outcome rates, by bounding the confidence using LOCC; the certification is semi-device-independent in that state preparation is trusted. We illustrate the demonstration and certification of NLWE for antiparallel qubit states. Our results make it feasible to experimentally realize NLWE using measurement devices with imperfections, such as non-unit detection efficiency, since maximum-confidence measurements rely only on detected events.

Comments
6 + 11 pages, 3 + 2 figures, typos corrected

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In this work, we present the framework for demonstrating and certifying the distinction between measurements in an entangled basis, called global measurements, and local operations and classical communication (LOCC), known as nonlocality without entanglement (NLWE). To be precise, we show NLWE via a maximum-confidence measurement in terms of a guess per detection event, called a confidence, a fine-grained guessing probability that encompasses both minimum-error and unambiguous state-discrimination strategies. We show that NLWE for unknown measurements can be certified, given the measurement-outcome rates, by bounding the confidence using LOCC; the certification is semi-device-independent in that state preparation is trusted. We illustrate the demonstration and certification of NLWE for antiparallel qubit states. Our results make it feasible to experimentally realize NLWE using measurement devices with imperfections, such as non-unit detection efficiency, since maximum-confidence measurements rely only on detected events.
Nonlocality without entanglement(NLWE) is a nonlocal phenomenon that occurs in quantum state discrimination of multipartite separable states. In the discrimination of orthogonal separable states, the term NLWE is used when the quantum states cannot be discriminated perfectly by local operations and classical communication. In this case, the occurrence of NLWE is independent of nonzero prior probabilities of quantum states being prepared. Recently, it has been found that the occurrence of NLWE can depend on nonzero prior probabilities in minimum-error discrimination of nonorthogonal separable states. Here, we show that even in optimal unambiguous discrimination, the occurrence of NLWE can depend on nonzero prior probabilities. We further show that NLWE can occur regardless of nonzero prior probabilities, even if only one state can be locally discriminated without error. Our results provide new insights into classifying sets of multipartite quantum states in terms of quantum state discrimination.
An ensemble of product states is said to exhibit “quantum nonlocality without entanglement” if it cannot be optimally discriminated using local operations and classical communication (LOCC). We show that this property can depend on the chosen discrimination measure. Specifically, we construct a family of ensembles, each consisting of six linearly independent, equally probable bipartite product states, for which LOCC fails to achieve optimal minimum-error discrimination but succeeds in achieving optimal unambiguous discrimination. We further extend our construction to multipartite systems and provide strong numerical evidence that a similar separation between local and global optima is present for minimum-error discrimination, but not for unambiguous discrimination.
We consider multipartite quantum state discrimination and provide a specific relation between the properties of entanglement witness and quantum nonlocality inherent in the confidence of measurement. We first provide the definition of the confidence of measurement as well as its useful properties for various types of multipartite measurement. We show that globally-maximum confidence that cannot be achieved by local operations and classical communication strongly depends on the existence of a certain type of entanglement witness. We also provide conditions for an upper bound on maximum of locally-achievable confidence. Finally, we establish a method in terms of entanglement witness to construct quantum state ensembles with nonlocal maximum confidence.
Nonlocality without entanglement(NLWE) is a nonlocal phenomenon that occurs in quantum state discrimination of multipartite separable states. Recently, it has been found that NLWE can depend on nonzero prior probabilities in minimum-error discrimination of nonorthogonal separable states. Here, we show that even in optimal unambiguous discrimination, NLWE can depend on nonzero prior probabilities. We further show that NLWE can occur regardless of nonzero prior probabilities, even if only one state can be locally discriminated without error. Our results provide new insights into classifying sets of multipartite quantum states in terms of quantum state discrimination.
Nonlocal correlations are useful for device-independent (DI) randomness certification (P ironio S. et al. , Nature (London) , 464 (2010) 1021). The advantage of this DI protocol over the conventional quantum protocol is that randomness can be certified even when experimental apparatuses are not trusted. Quantum entanglement is the necessary physical source for the nonlocal correlation required for such DI task. However, nonlocality and entanglement are distinct concepts. There exist entangled states which produce no nonlocal correlation and hence are not useful for the DI randomness certification task. Here we introduce the measurement-device–independent randomness certification task where one has trusted quantum state preparation devices but the mesurement devices are completely unspecified. Interestingly we show that there exist entangled states, with local description, that are a useful resource in such task but are useless in the corresponding DI scenario.
Bipartite quantum states with higher Schmidt numbers have been shown to outperform those with lower Schmidt numbers in various quantum information-processing tasks, highlighting the operational advantage of entanglement dimensionality. Certifying the Schmidt number of such states is therefore crucial for efficient resource utilization. Ideally, this certification should rely as little as possible on the certifying devices to ensure robustness against their potential imperfections. Fully device-independent certification via Bell-nonlocal games offers strong robustness but suffers from fundamental limitations: It cannot certify the Schmidt number of all entangled states. We demonstrate that this insufficiency of Bell-nonlocal games is not limited to entangled states that do not exhibit Bell nonlocality. Specifically, we prove the existence of Bell-nonlocal states whose Schmidt number cannot be certified by any Bell-nonlocal game when the parties are restricted to local projective measurements. To overcome this, we develop a measurement-device-independent certification method based on semiquantum nonlocal games, which assume trusted preparation devices but treat measurement devices as black boxes. We prove that for any bipartite state with a Schmidt number exceeding rrr, a semiquantum nonlocal game exists that can certify its Schmidt number. Finally, we provide an explicit construction of such a semiquantum nonlocal game based on an optimal Schmidt number witness operator.