Device-independent secret sharing and a stronger form of Bell nonlocality

Bell nonlocality, the fact that local hidden variable models cannot reproduce\nthe correlations obtained by measurements on entangled states, is a cornerstone\nin our modern understanding of quantum theory. Apart from its fundamental\nimplications, nonlocality is also at the core of device-independent quantum\ninformation processing, which successful implementation is achieved without\nprecise knowledge of the physical apparatus. Here we show that a stronger form\nof Bell nonlocality, for which even nonlocal hidden variable models cannot\nreproduce the quantum predictions, allows for the device-independent\nimplementation of secret sharing, a paradigmatic communication protocol where a\nsecret split amidst many possibly untrusted parts can only be decoded if they\ncollaborate among themselves.\n