Device-independent quantum secret sharing in arbitrary even dimensions

We present a device-independent quantum secret sharing scheme in arbitrary even dimension. We propose a d-dimensional N-partite linear game, utilizing a generic multipartite higher-dimensional Bell inequality, a generalization of Mermin's inequality in a higher dimension. The probability of winning this linear game defines the device-independence test in the proposed scheme. The security is proved under a causal independence assumption on measurement devices and it is based on the polygamy property of entanglement. By defining epsilon(cor) correctness and epsilon(c) completeness for a quantum secret sharing scheme, we also show that the proposed scheme is epsilon(cor) correct and epsilon(c) complete.