论文标题
通过量子准概率分布目睹非马克维亚性
Witnessing non-Markovianity by Quantum Quasi-Probability Distributions
论文作者
论文摘要
我们采用由排名一号投影仪（即纯量子状态）及其诱导的信息完成量子测量（IC-POVM）组成的框架，通过准概率分布来表示通常混合的量子状态。对于有限维系统上的离散帧，这会导致诸如准概率矢量的矢量代表，而对于连续变量（CV）系统中连贯状态的连续框架，该方法直接导致Glauber-Sudarshan p-runctions and Husimi Q-runctions and Hushimi Q-runctions的庆祝代表。我们解释说，这些准概率分布之间的kolmogorov距离导致痕量距离的上和下边界，从而测量了量子状态的区分性。我们将这些结果应用于开放量子系统的动力学，并基于P-和Q-功能的Kolmogorov距离构建非马克维亚性证人。通过几个示例，我们讨论了这位证人的表现，并证明它在高熵状态的制度中很有用，在高熵状态下，对痕量距离的直接评估通常非常苛刻。对于CV系统中的高斯动力学，我们甚至基于p功能之间的kolmogorov距离找到了合适的非马克维亚度度量，可以将其用作非高斯性的见证人。
We employ frames consisting of rank-one projectors (i.e. pure quantum states) and their induced informationally complete quantum measurements (IC-POVMs) to represent generally mixed quantum states by quasi-probability distributions. In the case of discrete frames on finite dimensional systems this results in a vector like representation by quasi-probability vectors, while for the continuous frame of coherent states in continuous variable (CV) systems the approach directly leads to the celebrated representation by Glauber-Sudarshan P-functions and Husimi Q-functions. We explain that the Kolmogorov distances between these quasi-probability distributions lead to upper and lower bounds of the trace distance which measures the distinguishability of quantum states. We apply these results to the dynamics of open quantum systems and construct a non-Markovianity witness based on the Kolmogorov distance of the P- and Q-functions. By means of several examples we discuss the performance of this witness and demonstrate that it is useful in the regime of high entropy states for which a direct evaluation of the trace distance is typically very demanding. For Gaussian dynamics in CV systems we even find a suitable non-Markovianity measure based on the Kolmogorov distance between the P-functions which can alternatively be used as a witness for non-Gaussianity.
