The Communication Value of a Quantum Channel
The Communication Value of a Quantum Channel
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DOI：
10.1109/tit.2022.3218540
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发表时间：
2021-09
影响因子：
2.5
通讯作者：
E. Chitambar;Ian George;Brian Doolittle;M. Junge
中科院分区：
文献类型：
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作者：
E. Chitambar;Ian George;Brian Doolittle;M. Junge
有各种方法来量化量子信道的通信能力。在这项工作中，我们引入了量子信道的通信值（cv），它描述了从其输出猜测信道输入的最佳概率。通过连接到以前的工作零错误信道模拟，我们表明，CV和它的纠缠辅助的变体也提供了双重解释，作为经典的通信成本完美地模拟不同方面的信道使用非信令资源。我们的研究涉及到通信值的特征作为一个广义的条件最小熵锥上的可分算子。使用这种表征，我们评估的CV为所有量子比特通道和高维通道具有一定的对称性。我们发现，任何纠缠打破通道具有乘法CV时，与任何其他通道并行使用，同样的是持有泡利通道和部分去极化通道。与此相反，CV被发现是非乘法的一个子集的著名的维尔纳-Holevo通道。这项工作的最后一个组成部分调查松弛的通道CV到其他锥，如一组运营商具有积极的部分转置（PPT）。
There are various ways to quantify the communication capabilities of a quantum channel. In this work we introduce the communication value (cv) of quantum channel, which describes the optimal probability of guessing the channel input from its output. By connecting to prior work on zero-error channel simulation, we show that the cv and its entanglement-assisted variant also offer dual interpretations as the classical communication cost for perfectly simulating different aspects of a channel using non-signaling resources. Our study involves characterizing the communication value as a generalized conditional min-entropy over the cone of separable operators. Using this characterization, we evaluate the cv for all qubit channels and higher-dimensional channels with certain symmetries. We find that the any entanglement-breaking channel has multiplicative cv when used in parallel with any other channel; the same is shown to hold for Pauli channels and partially depolarizing channels. In contrast, the cv is found to be non-multiplicative for a subset of the well-known Werner-Holevo channels. A final component of this work investigates relaxations of the channel cv to other cones such as the set of operators having a positive partial transpose (PPT).