We discuss discrete Weyl channels (DWCs) with correlated noise in consecutive uses. Some special cases of DWCs have been shown to have the so-called transition behavior, where the optimal signal states, which maximize the Holevo information between the transmitter and the receiver, sharply transition from product states to maximally entangled states as the degree of memory between the consecutive channel uses increases from a threshold value. We first show the general existence of this transition behavior for a class of DWCs where the product states are optimal for the memoryless case. We also provide two methods to estimate the degree of memory exhibited by the correlated noise. These estimators rely on generating classical data by measuring the channel output which shows the same memory characteristics as the consecutive uses of the channel. We specifically consider the Markovian noise but one of our proposed estimators can be straightforwardly generalized to an arbitrary type of noise as it provides the direct access to the sequence in which noise affects the consecutive input states.

中文翻译：

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具有马尔可夫记忆的离散外尔通道

我们讨论了在连续使用中具有相关噪声的离散外尔通道 (DWC)。DWC 的一些特殊情况已被证明具有所谓的过渡行为，其中最佳信号状态，最大化发射器和接收器之间的 Holevo 信息，从产品状态急剧过渡到最大纠缠状态作为之间的记忆程度连续通道使用从阈值增加。我们首先展示了一类 DWC 的这种转换行为的普遍存在，其中产品状态对于无记忆情况是最佳的。我们还提供了两种方法来估计相关噪声表现出的记忆程度。这些估计器依赖于通过测量通道输出来生成经典数据，该输出显示与通道的连续使用相同的记忆特性。