Approaches for approximate additivity of the Holevo information of quantum channels
Approaches for approximate additivity of the Holevo information of quantum channels
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DOI：
10.1103/physreva.97.012332
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发表时间：
2018-01-25
影响因子：
2.9
通讯作者：
Wilde, Mark M.
中科院分区：
文献类型：
--
作者：
Leditzky, Felix;Kaur, Eneet;Wilde, Mark M.
我们研究的量子通道，接近另一个通道的弱加性Holevo信息，我们推导出其经典容量的上界。具有弱加性Holevo信息的通道的示例是纠缠破坏通道、单位量子比特通道和Hadamard通道。与近似降解性的方法相关，我们为上面的每个类定义近似参数，这些参数测量任意通道与满足相应属性的接近程度。这给我们的经典容量的近似参数的函数，以及一个量子通道的动态容量区域的外部边界的上限。由于这些参数是根据菱形距离定义的，因此可以使用半定规划（SDP）有效地计算上界。我们展示了我们的方法的有用性与两个示例通道：一个凸混合的振幅阻尼和去极化噪声和振幅阻尼和失相噪声的组合物。对于这两个渠道，我们的界限表现良好，在某些制度的噪声参数相比，最近推导的SDP上界的经典容量。沿着的方式，我们定义了广义信道发散的概念（其中包括钻石距离作为一个例子），我们证明，联合协变信道这些数量最大化的协方差组下的状态不变的纯化。这后一结果可能是独立的利益。
We study quantum channels that are close to another channel with weakly additive Holevo information, and we derive upper bounds on their classical capacity. Examples of channels with weakly additive Holevo information are entanglement-breaking channels, unital qubit channels, and Hadamard channels. Related to the method of approximate degradability, we define approximation parameters for each class above, which measure how close an arbitrary channel is to satisfying the respective property. This gives us upper bounds on the classical capacity in terms of functions of the approximation parameters, as well as an outer bound on the dynamic capacity region of a quantum channel. Since these parameters are defined in terms of the diamond distance, the upper bounds can be computed efficiently using semidefinite programming (SDP). We exhibit the usefulness of our method with two example channels: a convex mixture of amplitude damping and depolarizing noise and a composition of amplitude damping and dephasing noise. For both channels, our bounds perform well in certain regimes of the noise parameters in comparison to a recently derived SDP upper bound on the classical capacity. Along the way, we define the notion of a generalized channel divergence (which includes the diamond distance as an example), and we prove that for jointly covariant channels these quantities are maximized by purifications of a state invariant under the covariance group. This latter result may be of independent interest.