Strengthened monotonicity of relative entropy via pinched Petz recovery map
Strengthened monotonicity of relative entropy via pinched Petz recovery map
复制标题
通过收缩 Petz 恢复图增强相对熵的单调性
DOI：
10.1109/tit.2016.2545680
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
A. Harrow
中科院分区：
文献类型：
--
作者：
David Sutter;M. Tomamichel;A. Harrow
两个状态之间的量子相对熵满足单调性，这意味着对两个状态应用相同的量子信道永远不会增加它们的相对熵。我们知道，只有当存在一个“恢复图”，精确地逆转量子信道对两种状态的影响时，这种不平等才会紧密。在本文中，我们通过表明相对熵的差异由第一状态和从其处理版本恢复的状态之间的测量相对熵的边界来加强这个不等式。恢复图是旋转佩兹恢复图的凸组合，完美地逆转了第二态上的量子通道。作为一种特殊情况，我们复制了最近的条件互信息下界，如[Fawzi和Renner， common]中证明的下界。数学。理论物理。, 2015]。我们的证明只依赖于捏缩映射和算子对数的初等性质。
The quantum relative entropy between two states satisfies a monotonicity property, meaning that applying the same quantum channel to both states can never increase their relative entropy. It is known that this inequality is only tight when there is a “recovery map” that exactly reverses the effects of the quantum channel on both states. In this paper we strengthen this inequality by showing that the difference of relative entropies is bounded below by the measured relative entropy between the first state and a recovered state from its processed version. The recovery map is a convex combination of rotated Petz recovery maps and perfectly reverses the quantum channel on the second state. As a special case we reproduce recent lower bounds on the conditional mutual information such as the one proved in [Fawzi and Renner, Commun. Math. Phys., 2015]. Our proof only relies on elementary properties of pinching maps and the operator logarithm.
影响因子：
8.6
作者：
F. Brandão;A. Harrow;J. Oppenheim;Sergii Strelchuk
通讯作者：
F. Brandão;A. Harrow;J. Oppenheim;Sergii Strelchuk