Compound channels, transition expectations, and liftings
Compound channels, transition expectations, and liftings
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DOI：
10.1007/s002459900097
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发表时间：
1999-01-01
影响因子：
1.8
通讯作者：
Ohya, M
中科院分区：
文献类型：
--
作者：
Accardi, L;Ohya, M
在第1节中，我们引入提升的概念作为在[21]和[22]中引入的复合态概念的推广，并且我们表明，这个概念允许统一的方法来解决量子测量和通过量子信道的信号传输问题。线性提升的对偶是[3]意义下的转移期望，我们刻画了[22]意义下的由复合态产生的转移期望.第二节刻画了值域包含在乘积态的闭凸船体中的提升，证明了相应的量子马尔可夫链[2]是由[4]中的量子随机游动和[3]中考虑的局部可对角化态的经典推广唯一确定的。在第4节中，作为上述结果的第一个应用，我们证明了在[21]中处理的光通信的衰减（分束）过程可以根据提升和跃迁期望以更简单和更一般的方式来描述。根据新的描述，重新导出了衰减过程中信息传输的错误概率。在压缩情形下，我们还得到了一些关于误差概率的显式计算的新结果。
In Section 1 we introduce the notion of lifting as a generalization of the notion of compound state introduced in [21] and [22] and we show that this notion allows a unified approach to the problems of quantum measurement and of signal transmission through quantum channels. The dual of a linear lifting is a transition expectation in the sense of [3] and we characterize those transition expectations which arise from compound states in the sense of [22].In Section 2 we characterize those liftings whose range is contained in the closed convex hull of product states and we prove that the corresponding quantum Markov chains [2] are uniquely determined by a classical generalization of both the quantum random walks of [4] and the locally diagonalizable states considered in [3].In Section 4, as a first application of the above results, we prove that the attenuation (beam splitting) process for optical communication treated in [21] can be described in a simpler and more general way in terms of liftings and of transition expectations. The error probabilty of information transmission in the attenuation process is rederived from our new description. We also obtain some new results concerning the explicit computation df error probabilities in the squeezing case.