纯化复杂性，无需纯化
Purification Complexity without Purifications
摘要：
我们将Fubini-Study方法推广到一般量子态，采用密度矩阵空间上的Bures度量或量子费舍尔信息度量作为复杂性度量.由于乌尔曼定理，我们表明，混合状态的复杂性完全等于纯化的复杂性所测量的Fubini研究度量的纯化状态，但没有明确应用任何纯化。我们还发现，在任何保迹量子操作下，纯化的复杂性都不会增加。我们还研究了混合高斯态作为一个例子，明确说明我们的结论纯化复杂性。
英文摘要：
We generalize the Fubini-Study method for pure-state complexity to generic quantum states by taking Bures metric or quantum Fisher information metric on the space of density matrices as the complexity measure. Due to Uhlmann's theorem, we show that the mixed-state complexity exactly equals the purification complexity measured by the Fubini-Study metric for purified states but without explicitly applying any purification. We also find the purification complexity is non-increasing under any trace-preserving quantum operations. We also study the mixed Gaussian states as an example to explicitly illustrate our conclusions for purification complexity.
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