Anza Fabio, Crutchfield James P
Department of Mathematics Informatics and Geoscience, University of Trieste, Via Alfonso Valerio 2, 34127 Trieste, Italy.
Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA.
Entropy (Basel). 2024 Mar 1;26(3):225. doi: 10.3390/e26030225.
Any given density matrix can be represented as an infinite number of ensembles of pure states. This leads to the natural question of how to uniquely select one out of the many, apparently equally-suitable, possibilities. Following Jaynes' information-theoretic perspective, this can be framed as an inference problem. We propose the Maximum Geometric Quantum Entropy Principle to exploit the notions of Quantum Information Dimension and Geometric Quantum Entropy. These allow us to quantify the entropy of fully arbitrary ensembles and select the one that maximizes it. After formulating the principle mathematically, we give the analytical solution to the maximization problem in a number of cases and discuss the physical mechanism behind the emergence of such maximum entropy ensembles.
任何给定的密度矩阵都可以表示为无限多个纯态系综。这就引出了一个自然的问题：如何从众多看似同样合适的可能性中唯一地选择一个。遵循杰恩斯的信息论观点，这可以被构建为一个推理问题。我们提出最大几何量子熵原理，以利用量子信息维度和几何量子熵的概念。这些使我们能够量化完全任意系综的熵，并选择使其最大化的系综。在对该原理进行数学表述之后，我们给出了一些情况下最大化问题的解析解，并讨论了这种最大熵系综出现背后的物理机制。
