论文标题
最大几何量子熵
Maximum Geometric Quantum Entropy
论文作者
论文摘要
任何给定的密度矩阵都可以表示为无限数量的纯状态集合。这导致了一个自然的问题，即如何在许多显然同样合适的可能性中唯一选择一个。遵循Jaynes的信息理论观点，这可以作为推理问题进行框架。我们提出了最大的几何量子熵原理，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合奏的熵，并选择最大化它的熵。在数学上制定原理后，我们在许多情况下为最大化问题提供了分析解决方案，并讨论了此类最大熵集合出现背后的物理机制。
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.
