Device-independent quantum secret sharing in arbitrary even dimensions
Sarbani Roy, Sourav Mukhopadhyay · Physical Review A · 2019
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 ${\ensuremath{\epsilon}}_{\mathrm{cor}}$ correctness and ${\ensuremath{\epsilon}}^{c}$ completeness for a quantum secret sharing scheme, we also show that the proposed scheme is ${\ensuremath{\epsilon}}_{\mathrm{cor}}$ correct and ${\ensuremath{\epsilon}}^{c}$ complete.