Self-testing was originally introduced as a device-independent method of certification of entangled quantum states and local measurements performed on them. Recently, in (Baccari etal 2020 Phys. Rev. Lett. 125 260507) the notion of state self-testing has been generalized to entangled subspaces and the first self-testing strategies for exemplary genuinely entangled subspaces have been given. The main aim of our work is to pursue this line of research and to address the question how ‘large’ (in terms of dimension) are genuinely entangled subspaces that can be self-tested, concentrating on the multiqubit stabilizer formalism. To this end, we first introduce a framework allowing to efficiently check whether a given stabilizer subspace is genuinely entangled. Building on it, we then determine the maximal dimension of genuinely entangled subspaces that can be constructed within the stabilizer subspaces and provide an exemplary construction of such maximally-dimensional subspaces for any number of qubits. Third, we construct Bell inequalities that are maximally violated by any entangled state from those subspaces and thus also any mixed states supported on them, and we show these inequalities to be useful for self-testing. Interestingly, our Bell inequalities allow for identification of higher-dimensional face structures in the boundaries of the sets of quantum correlations in the simplest multipartite Bell scenarios in which every observer performs two dichotomic measurements.

自测试最初是作为一种独立于设备的方法来验证纠缠量子态和对它们执行的局部测量。最近，在 (Baccari et al 2020 Phys. Rev. Lett. 125260507）状态自测的概念已被推广到纠缠子空间，并且已经给出了示例性真正纠缠子空间的第一个自测策略。我们工作的主要目的是进行这一研究，并解决可以自我测试的真正纠缠子空间有多大（就维度而言）“大”的问题，专注于多量子位稳定器形式主义。为此，我们首先引入一个框架，允许有效地检查给定的稳定子空间是否真正纠缠。在此基础上，我们然后确定可以在稳定器子空间内构建的真正纠缠子空间的最大维数，并为任意数量的量子位提供此类最大维子空间的示例性构造。第三，我们构造了贝尔不等式，这些不等式被这些子空间中的任何纠缠状态以及它们支持的任何混合状态最大程度地违反，并且我们证明这些不等式对自检很有用。有趣的是，我们的贝尔不等式允许在最简单的多部分贝尔场景中识别量子相关集边界中的高维人脸结构，其中每个观察者都进行两次二分测量。