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arXiv · 1501.01746

State-independent contextuality sets for a qutrit

Zhen-Peng Xu·Jing-Ling Chen·Hong-Yi Su
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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.

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Zhen-Peng Xu, Jing-Ling Chen, Hong-Yi Su. 2015-01-08. State-independent contextuality sets for a qutrit. https://arxiv.org/abs/1501.01746

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