Felice Domenico, Mancini Stefano, Ay Nihat
Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany.
School of Science and Technology, University of Camerino, I-62032 Camerino, Italy.
Entropy (Basel). 2019 Apr 24;21(4):435. doi: 10.3390/e21040435.
A new canonical divergence is put forward for generalizing an information-geometric measure of complexity for both classical and quantum systems. On the simplex of probability measures, it is proved that the new divergence coincides with the Kullback-Leibler divergence, which is used to quantify how much a probability measure deviates from the non-interacting states that are modeled by exponential families of probabilities. On the space of positive density operators, we prove that the same divergence reduces to the quantum relative entropy, which quantifies many-party correlations of a quantum state from a Gibbs family.
提出了一种新的典范散度，用于推广经典和量子系统复杂性的信息几何度量。在概率测度的单纯形上，证明了新散度与库尔贝克 - 莱布勒散度一致，后者用于量化概率测度与由概率指数族建模的非相互作用态的偏离程度。在正密度算子空间上，我们证明相同的散度简化为量子相对熵，它从吉布斯族量化量子态的多方关联。
