Virtually all of the analysis of quantum contextuality is restricted to the case where events are represented by rank-one projectors. This restriction is arbitrary and not motivated by physical considerations. We show here that loosening the rank constraint opens a new realm of quantum contextuality and we demonstrate that state-independent contextuality (SIC) can even require projectors of nonunit rank. This enables the possibility of SIC with less than 13 projectors, which is the established minimum for the case of rank one. We prove that for any rank, at least 9 projectors are required. Furthermore, in an exhaustive numerical search we find that 13 projectors are also minimal for the cases where all projectors are uniformly of rank two or uniformly of rank three.

几乎所有对量子上下文的分析都仅限于事件由一级投影仪表示的情况。这种限制是任意的，并非出于物理考虑。我们在这里展示了放宽秩约束打开了量子上下文的新领域，并且我们证明了状态独立上下文 (SIC) 甚至可能需要非单位秩的投影仪。这使得使用少于 13 个投影仪的 SIC 成为可能，这是 rank 1 情况下确定的最小值。我们证明，对于任何等级，至少需要 9 台投影仪。此外，在详尽的数值搜索中，我们发现对于所有投影仪都统一为 2 级或统一为 3 的情况，13 台投影仪也是最少的。