标题： 向全分类全息熵不等式的迈进 显示英文标题

标题： Towards a complete classification of holographic entropy inequalities

摘要： 我们提出一种确定性方法，以找到所有具有对应收缩映射的全息熵不等式，并论证我们方法的完备性。 我们利用全息熵不等式、收缩映射和部分立方体之间的三重性。 更具体地说，全息熵不等式的有效性由收缩映射的存在性所暗示，我们证明这等价于找到一个收缩图的等距嵌入。 因此，凭借所论证的收缩映射证明方法的完备性，找到所有全息熵不等式的问题等价于找到所有收缩映射的问题，我们将这一问题转化为找到所有图像图部分立方体的问题。 我们给出了该问题的算法解决方案，并描述了我们方法的复杂性。 我们还展示了有趣的副产品，最显著的是生成候选量子熵不等式的程序。 显示英文摘要

摘要： We propose a deterministic method to find all holographic entropy inequalities that have corresponding contraction maps and argue the completeness of our method. We use a triality between holographic entropy inequalities, contraction maps and partial cubes. More specifically, the validity of a holographic entropy inequality is implied by the existence of a contraction map, which we prove to be equivalent to finding an isometric embedding of a contracted graph. Thus, by virtue of the argued completeness of the contraction map proof method, the problem of finding all holographic entropy inequalities is equivalent to the problem of finding all contraction maps, which we translate to a problem of finding all image graph partial cubes. We give an algorithmic solution to this problem and characterize the complexity of our method. We also demonstrate interesting by-products, most notably, a procedure to generate candidate quantum entropy inequalities.