State-independent contextuality sets for a qutrit

TL;DR

This paper introduces a generalized set of complex rays for a qutrit system, expanding the understanding of state-independent contextuality and its applications in quantum information processing.

Contribution

It generalizes known SIC sets using a parameterized family of complex rays, proving SIC properties for specific values of the parameter.

Findings

Sets with k=3m and k=4 are SIC.

Set with k=5 is not SIC.

Generalized rays enrich SIC proof and quantum info applications.

Abstract

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, 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.