State-independent contextuality sets for a qutrit

We present a generalized set of complex rays for a qutrit in terms of parameter q = e(i2 pi/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 sets, while the set with k = 5 is not. Our generalized set of rays will theoretically enrich the study of SIC proofs, and stimulate the novel application to quantum information processing. (C) 2015 Elsevier B.V. All rights reserved.