Given a Bell inequality, if its maximal quantum violation can be achieved only by a single set of measurements for each party or a single quantum state, up to local unitaries, one refers to such a phenomenon as self-testing. For instance, the maximal quantum violation of the Clauser-Horne-Shimony-Holt inequality certifies that the underlying state contains the two-qubit maximally entangled state and the measurements of one party contains a pair of anti-commuting qubit observables. As a consequence, the other party automatically verifies the set of states remotely steered, namely the "assemblage", is in the eigenstates of a pair of anti-commuting observables. It is natural to ask if the quantum violation of the Bell inequality is not maximally achieved, or if one does not care about self-testing the state or measurements, are we capable of estimating how close the underlying assemblage is to the reference one? In this work, we provide a systematic device-independent estimation by proposing a framework called "robust self-testing of steerable quantum assemblages". In particular, we consider assemblages violating several paradigmatic Bell inequalities and obtain the robust self-testing statement for each scenario. Our result is device-independent (DI), i.e., no assumption is made on the shared state and the measurement devices involved. Our work thus not only paves a way for exploring the connection between the boundary of quantum set of correlations and steerable assemblages, but also provides a useful tool in the areas of DI quantum certification. As two explicit applications, we show 1) that it can be used for an alternative proof of the protocol of DI certification of all entangled two-qubit states proposed by Bowles et al., and 2) that it can be used to verify all non-entanglement-breaking qubit channels with fewer assumptions compared with the work of Rosset et al.

中文翻译：

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可控量子组合的鲁棒自测及其在独立于设备的量子认证中的应用

给定一个贝尔不等式，如果它的最大量子违反只能通过对每一方或单个量子状态的一组测量来实现，直到局部幺正，人们将这种现象称为自检。例如，Clauser-Horne-Shimony-Holt 不等式的最大量子违反证明了基础状态包含两个量子位的最大纠缠态，并且一方的测量值包含一对反交换量子位可观测值。因此，另一方自动验证远程引导的状态集，即“组合”，是否处于一对反通勤可观察量的本征态。很自然地会问，贝尔不等式的量子违反是否没有最大程度地实现，或者人们是否不关心自我测试状态或测量，我们是否能够估计基础组合与参考组合的接近程度？在这项工作中，我们通过提出一个称为“可控量子组合的鲁棒自测试”的框架来提供系统的设备独立估计。特别是，我们考虑了违反几个范式贝尔不等式的组合，并为每个场景获得了强大的自测语句。我们的结果是与设备无关的 (DI)，即没有对共享状态和所涉及的测量设备进行假设。因此，我们的工作不仅为探索相关性量子集边界与可控组合之间的联系铺平了道路，而且还为 DI 量子认证领域提供了有用的工具。作为两个显式应用，