任意量子测量的极值分解
Decomposition of any quantum measurement into extremals
摘要：
我们设计了一个有效的和建设性的算法来分解任何广义量子测量到一个凸组合的极值测量。我们表明，如果允许一个经典的后处理步骤，只需要极值秩1 POVM。对于在$d$维空间上具有$N$元素的测量，我们的算法将其分解为至多$(N-1)d+1$极值，而先前已知的最佳上限缩放为$d^2$。由于分解不是唯一的，我们展示了如何调整我们的算法，以提供特定类型的分解，表现出一些所需的属性。
英文摘要：
We design an efficient and constructive algorithm to decompose any generalized quantum measurement into a convex combination of extremal measurements. We show that if one allows for a classical post-processing step only extremal rank-1 POVMs are needed. For a measurement with $N$ elements on a $d$-dimensional space, our algorithm will decompose it into at most $(N-1)d+1$ extremals, whereas the best previously known upper bound scaled as $d^2$. Since the decomposition is not unique, we show how to tailor our algorithm to provide particular types of decompositions that exhibit some desired property.
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