论文标题
纯化复杂性而无需净化
Purification Complexity without Purifications
论文作者
论文摘要
我们通过将Bures公制或量子Fisher Information指标在密度矩阵的空间作为复杂度度量中概括为通用量子状态的Fubini研究方法。由于Uhlmann的定理，我们表明混合状态的复杂性完全等于纯化状态的Fubini-study Metric测得的纯化复杂性，但没有明确应用任何纯化。我们还发现，在任何痕量保护的量子操作下，纯化复杂性是不侵入的。我们还研究混合高斯国家的一个例子，以明确说明我们的纯化复杂性结论。
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.
