State-independent contextuality sets for a qutrit

الأصل · EN

We present a generalized set of complex rays for a qutrit in terms of parameter q=eⁱ²π/ᵏ, a k-th root of unity. Remarkably, when k=2,3, the set reduces to two well known state-independent contextuality (SIC) sets: the Yu-Oh set and the Bengtsson-Blanchfield-Cabello set. Based on the Ramanathan-Horodecki criterion and the violation of a noncontextuality inequality, we have proven that the sets with k=3m and k=4 are SIC, while the set with k=5 is not. Our generalized set of rays will theoretically enrich the study of SIC proof, and experimentally stimulate the novel application to quantum information processing.