论文标题
量子相对熵的最佳自我屏障
Optimal self-concordant barriers for quantum relative entropies
论文作者
论文摘要
量子相对熵是两个正定矩阵的共同凸功能，这些矩阵概括了kullback-leibler差异，并且在量子信息理论中自然出现。在本文中，我们证明了各种量子相对熵和差异的题词的自然屏障函数的自然障碍。此外，我们表明这些屏障具有最佳的屏障参数。这些屏障允许使用涉及量子相对熵的凸优化问题，可以使用用于非对称锥体的内点方法直接求解，避免了以前方法中使用的近似值和提升技术。更一般而言，我们为与操作员凹函数的非交通性观点相关的各种封闭凸锥的自然屏障建立了自然屏障的自我联系，并表明所得的屏障参数是最佳的。
Quantum relative entropies are jointly convex functions of two positive definite matrices that generalize the Kullback-Leibler divergence and arise naturally in quantum information theory. In this paper, we prove self-concordance of natural barrier functions for the epigraphs of various quantum relative entropies and divergences. Furthermore we show that these barriers have optimal barrier parameter. These barriers allow convex optimization problems involving quantum relative entropies to be directly solved using interior point methods for non-symmetric cones, avoiding the approximations and lifting techniques used in previous approaches. More generally, we establish the self-concordance of natural barriers for various closed convex cones related to the noncommutative perspectives of operator concave functions, and show that the resulting barrier parameters are optimal.
