论文标题
定义SIC POVM所需的最小条件是什么？
What are the minimal conditions required to define a SIC POVM?
论文作者
论文摘要
对称信息完整（SIC）POVM是一类量子测量值，除了信息完成外，还满足三个条件：1）每个POVM元素均为等级一，2）Hilbert-Schmidt在任意两个不同的元素之间的内部产物是恒定的，而3）每个元素的痕迹是恒定的。第三个条件通常被忽略，因为它可能给人的印象是从第二个开始效力。我们表明，该条件无法删除，因为它导致了POVM元素的轨迹的两个不同值。这一观察结果使我们定义了一类更广泛的测量结果，我们称之为半SIC POVM。在第二个维度中，我们表明存在半奇异的POVM，我们建立了整个家庭。在较高的维度中，我们表征了半Sic POVM的关键属性和应用，并注意其存在的证据保持开放。
Symmetric informationally complete (SIC) POVMs are a class of quantum measurements which, in addition to being informationally complete, satisfy three conditions: 1) every POVM element is rank one, 2) the Hilbert-Schmidt inner product between any two distinct elements is constant, and 3) the trace of each element is constant. The third condition is often overlooked, since it may give the impression that it follows trivially from the second. We show that this condition cannot be removed, as it leads to two distinct values for the trace of an element of the POVM. This observation has led us to define a broader class of measurements which we call semi-SIC POVMs. In dimension two we show that semi-SIC POVMs exist, and we construct the entire family. In higher dimensions, we characterize key properties and applications of semi-SIC POVMs, and note that the proof of their existence remains open.
