论文标题
量子相对熵的积分公式意味着数据处理不等式
Integral formula for quantum relative entropy implies data processing inequality
论文作者
论文摘要
Integral representations of quantum relative entropy, and of the directional second and higher order derivatives of von Neumann entropy, are established, and used to give simple proofs of fundamental, known data processing inequalities: the Holevo bound on the quantity of information transmitted by a quantum communication channel, and, much more generally, the monotonicity of quantum relative entropy under trace-preserving positive linear maps -- complete positivity of the map need not be假设。后者的结果首先是由Müller-Hermes和Reeb根据Beigi的工作证明的。为了简单地应用此类单调性，我们考虑了在量子测量中不侵入的任何“差异”，例如von Neumann熵的凹度或各种已知的量子差异。由于Hiai，Ohya和Tsukada引起的一个优雅的论点是用来表明具有规定痕量距离的量子状态上这样的“分歧”的最低限度与成对二进制经典状态的相应亲本相同。还讨论了新的积分公式在信息理论的一般概率模型中的应用，以及经典rényi差异的相关积分公式。
Integral representations of quantum relative entropy, and of the directional second and higher order derivatives of von Neumann entropy, are established, and used to give simple proofs of fundamental, known data processing inequalities: the Holevo bound on the quantity of information transmitted by a quantum communication channel, and, much more generally, the monotonicity of quantum relative entropy under trace-preserving positive linear maps -- complete positivity of the map need not be assumed. The latter result was first proved by Müller-Hermes and Reeb, based on work of Beigi. For a simple application of such monotonicities, we consider any `divergence' that is non-increasing under quantum measurements, such as the concavity of von Neumann entropy, or various known quantum divergences. An elegant argument due to Hiai, Ohya, and Tsukada is used to show that the infimum of such a `divergence' on pairs of quantum states with prescribed trace distance is the same as the corresponding infimum on pairs of binary classical states. Applications of the new integral formulae to the general probabilistic model of information theory, and a related integral formula for the classical Rényi divergence, are also discussed.
