We continue our numerical study of quantum belief propagation initiated in [Phys. Rev. A, 77 (2008), p. 052318]. We demonstrate how the method can be expressed in terms of an effective thermal potential that materializes when the system presents quantum correlations, but is insensitive to classical correlations. The thermal potential provides an efficient means to assess the precision of belief propagation on graphs with no loops. We illustrate these concepts using the one-dimensional quantum Ising model and compare our results with exact solutions. We also use the method to study the transverse field quantum Ising spin glass for which we obtain a phase diagram that is largely in agreement with the one obtained in [arXiv:0706.4391] using a different approach. Finally, we introduce the coarse grained belief propagation (CGBP) algorithm to improve belief propagation at low temperatures. This method combines the reliability of belief propagation at high temperatures with the ability of entanglement renormalization to efficiently describe low energy subspaces of quantum systems with local interactions. With CGBP, thermodynamic properties of quantum systems can be calculated with a high degree of accuracy at all temperatures.
Classical predictability and coarse-grained evolution of the quantum baker's map
我们研究如何经典预测的粗粒度演化的量子面包师映射依赖于粗粒度的字符。我们的分析将Brun和Hartle [Phys. Rev. D 60，123503（1999）]的早期工作扩展到混沌映射的情况。为了量化的可预测性，我们比较了一个家庭的粗粒度的退相干历史形式主义的熵增加率。我们发现，熵增加的速率是由表征粗粒化的尺度的数量占主导地位。
Mutually Unbiased Coarse-Grained Measurements of Two or More Phase-Space Variables
相空间算符本征态的相互无偏性，如位置和动量，或它们的标准粗粒化版本，只存在于无限压缩的极限情况下。在[Phys. Rev. Lett. 120，040403（2018）]表明，对于这两个算子的周期性粗粒化，可以恢复相互无偏性。在这里，我们调查的相互无偏的粗粒度测量两个以上的相空间变量。我们发现，相互无偏性可以恢复之间的任何两个非平行的相空间运营商的周期性粗粒化。我们说明了这些结果，通过光学实验，使用分数傅里叶变换来制备和测量相互无偏的相空间变量。两个和三个相互无偏测量之间的差异进行了讨论。我们的结果有助于弥合连续和离散量子力学之间的差距，并可能是有用的量子信息协议。
