论文标题
关于查找最大熵兼容量子状态的复杂性
On the complexity of finding the maximum entropy compatible quantum state
论文作者
论文摘要
本文中，我们研究了从一组兼容的边缘恢复密度运算符的问题，这是由于物理观察的局限性所激发的。鉴于一组兼容密度运算符并非单数，因此我们采用Jaynes的原理，并希望表征具有最大熵的兼容密度运算符。我们首先表明，即使对于最简单的3链，比较兼容密度运算符的熵也是QSZK算法。然后，我们专注于量子马尔可夫链和树的特定情况，并确定在这些情况下，存在一个量子多项式电路，该电路构建了最大熵兼容密度算子。最后，我们将Chow-Liu算法扩展到量子状态的同一子类。
Herein we study the problem of recovering a density operator from a set of compatible marginals, motivated from limitations of physical observations. Given that the set of compatible density operators is not singular, we adopt Jaynes' principle and wish to characterize a compatible density operator with maximum entropy. We first show that comparing the entropy of compatible density operators is QSZK-complete, even for the simplest case of 3-chains. Then, we focus on the particular case of quantum Markov chains and trees and establish that for these cases, there exists a quantum polynomial circuit that constructs the maximum entropy compatible density operator. Finally, we extend the Chow-Liu algorithm to the same subclass of quantum states.
