量子信道的本征值反问题
The inverse eigenvalue problem for quantum channels
摘要：
给出一个n个复数的列表，它什么时候可以是一个量子信道的频谱，即，一个完全正的保迹映射我们提供了一个明确的解决方案，为n=4的情况下，并表明，在一般的频谱的非零部分的特征，基本上可以给出在其经典的对应-随机矩阵的非零频谱。经典和量子的情况下，给出了详细的比较。我们讨论了我们的发现在时间序列和关联函数分析中的应用，并提供了外围频谱的一般特征，即，模1的特征值集合。我们表明，虽然周边的本征系统具有相同的结构，所有的施瓦茨映射，施加在其余的频谱立即改变，如果一个离开完全积极的约束。
英文摘要：
Given a list of n complex numbers, when can it be the spectrum of a quantum channel, i.e., a completely positive trace preserving map? We provide an explicit solution for the n=4 case and show that in general the characterization of the non-zero part of the spectrum can essentially be given in terms of its classical counterpart - the non-zero spectrum of a stochastic matrix. A detailed comparison between the classical and quantum case is given. We discuss applications of our findings in the analysis of time-series and correlation functions and provide a general characterization of the peripheral spectrum, i.e., the set of eigenvalues of modulus one. We show that while the peripheral eigen-system has the same structure for all Schwarz maps, the constraints imposed on the rest of the spectrum change immediately if one departs from complete positivity.
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