寻找最大熵相容量子态的复杂性
On the complexity of finding the maximum entropy compatible quantum state
摘要：
在这里，我们研究的问题，从一组兼容的边缘恢复的密度算子，从物理观测的限制。在相容密度算子集不奇异的条件下，我们采用Jaynes原理刻画了相容密度算子的极大熵。我们首先表明，比较相容密度算子的熵是QSZK-完全的，即使是最简单的情况下的3链。然后，我们专注于量子马尔可夫链和树的特殊情况下，并建立，对于这些情况下，存在一个量子多项式电路，构造最大熵相容的密度算子。最后，我们将Chow-Liu算法推广到同一子类的量子态。
英文摘要：
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.
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