Self-testing is a device-independent method that usually amounts to show that the maximal quantum violation of a Bell’s inequality certifies a unique quantum state, up to some symmetries inherent to the device-independent framework. In this work, we enlarge this approach and show how a coarse-grained version of self-testing is possible in which physically relevant properties of a many-body system are certified. To this aim we study a Bell scenario consisting of an arbitrary number of parties and show that the membership to a set of (entangled) quantum states whose size grows exponentially with the number of parties can be self-tested. Specifically, we prove that a many-body generalization of the chained Bell inequality is maximally violated if and only if the underlying quantum state is equal, up to local isometries, to a many-body singlet. The maximal violation of the inequality therefore certifies any statistical mixture of the exponentially many orthogonal pure states spanning the singlet manifold.

中文翻译：

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粗粒度自测

自测试是一种独立于设备的方法，通常表明贝尔不等式的最大量子违反证明了独特的量子态，达到独立于设备的框架固有的一些对称性。在这项工作中，我们扩大了这种方法，并展示了如何进行粗粒度版本的自测，其中多体系统的物理相关属性得到认证。为此，我们研究了一个由任意数量的参与方组成的贝尔场景，并表明可以自测其大小随参与方数量呈指数增长的一组（纠缠）量子态的成员资格。具体来说，我们证明了链式贝尔不等式的多体泛化当且仅当基础量子态等于多体单线态，直到局部等距。