论文标题
与国家独立的量子上下文，具有非单元等级的投影仪
State-independent quantum contextuality with projectors of nonunit rank
论文作者
论文摘要
实际上，量子上下文性的所有分析都仅限于事件由排名一号投影仪代表的情况。这种限制是任意的，不是由身体考虑的动机。我们在这里表明，放松等级约束开启了量子上下文的新领域，我们证明了与国家无关的上下文性甚至可以要求非单元等级的投影仪。这使得具有少于13个投影仪的国家独立背景性的可能性，这是等级第一案例的最低限度。我们证明，对于任何等级，至少需要9个投影仪。此外，在详尽的数值搜索中，我们发现13个投影仪在所有投影仪均匀分别为第二等级或均匀排名第三的情况下也是最小的。
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 can even require projectors of nonunit rank. This enables the possibility of state-independent contextuality 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.
