论文标题
相干状态在一般CCR代数上的相对熵
Relative entropy of coherent states on general CCR algebras
论文作者
论文摘要
对于通用CCR代数的子代数，我们考虑了一般（不一定是纯）的准式态与相干激发之间的相对熵。我们从单粒子模块数据方面为此熵提供了一个统一的公式。此外，我们研究了沿着互联母子空间家族增加的沿亚代毛的相对熵的变化。在这里，熵的凸度（通常考虑到量子无效条件）被第二个衍生物的估计值较低，由“批量项”和“边界项”组成。我们的主要假设是子空间处于不同的模块化位置，这是一种规律性条件，可以概括半侧模块化夹杂物的通常概念。我们在相关示例中说明了我们的结果，包括共形$ u（1）$ - 当前的热状态。
For a subalgebra of a generic CCR algebra, we consider the relative entropy between a general (not necessarily pure) quasifree state and a coherent excitation thereof. We give a unified formula for this entropy in terms of single-particle modular data. Further, we investigate changes of the relative entropy along subalgebras arising from an increasing family of symplectic subspaces; here convexity of the entropy (as usually considered for the Quantum Null Energy Condition) is replaced with lower estimates for the second derivative, composed of "bulk terms" and "boundary terms". Our main assumption is that the subspaces are in differential modular position, a regularity condition that generalizes the usual notion of half-sided modular inclusions. We illustrate our results in relevant examples, including thermal states for the conformal $U(1)$-current.
