反射正性的熵不等式
Entropy inequalities from reflection positivity
摘要：
本文研究了在量子场论中，真空态的熵和Renyi熵是否可以用量子化子表示的问题。在这种情况下，正性关系的映射成不等式的熵。我们使用反射正性的实时版本来编写它们，这可以推广到一般的量子系统。利用这一推广，我们可以证明整数指标的Renyi熵所服从的一个无穷不等式序列。有一个独立的不等式涉及任何数量的不同的子系统。在量子场论中，这些不等式具有简单的几何形式，并且与欧氏公式中由扭转算符的真空期望值给出的整数指数Renyi熵一致.几个可能的概括和具体的例子进行了分析。
英文摘要：
We investigate the question of whether the entropy and the Renyi entropies of the vacuum state reduced to a region of the space can be represented in terms of correlators in quantum field theory. In this case, the positivity relations for the correlators are mapped into inequalities for the entropies. We write them using a real time version of reflection positivity, which can be generalized to general quantum systems. Using this generalization we can prove an infinite sequence of inequalities which are obeyed by the Renyi entropies of integer index. There is one independent inequality involving any number of different subsystems. In quantum field theory the inequalities acquire a simple geometrical form and are consistent with the integer index Renyi entropies being given by vacuum expectation values of twisting operators in the Euclidean formulation. Several possible generalizations and specific examples are analyzed.
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