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首页> 外文期刊>IEEE Transactions on Information Theory >Superadditivity of Quantum Channel Coding Rate With Finite Blocklength Joint Measurements
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Superadditivity of Quantum Channel Coding Rate With Finite Blocklength Joint Measurements

机译：有限块长联合测量的量子信道编码率的超可加性

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摘要

The maximum rate at which classical information can be reliably transmitted per use of a quantum channel strictly increases in general with N , the number of channel outputs that are detected jointly by the quantum joint-detection receiver (JDR). This phenomenon is known as superadditivity of the maximum achievable information rate over a quantum channel. We study this phenomenon for a pure-state classical-quantum channel and provide a lower bound on CN/N, the maximum information rate when the JDR is restricted to making joint measurements over no more than N quantum channel outputs, while allowing arbitrary classical error correction. We also show the appearance of a superadditivity phenomenon-of mathematical resemblance to the aforesaid problem-in the channel capacity of a classical discrete memoryless channel when a concatenated coding scheme is employed, and the inner decoder is forced to make hard decisions on N -length inner codewords. Using this correspondence, we develop a unifying framework for the above two notions of superadditivity, and show that for our lower bound to CN/N to be equal to a given fraction of the asymptotic capacity C of the respective channel, N must be proportional to V/C2 , where V is the respective channel dispersion quantity.
机译：通常，随着量子连接检测接收机（JDR）共同检测到的通道输出数量N的增加，每次使用量子通道可以可靠地传输经典信息的最大速率通常会严格提高。这种现象被称为量子通道上最大可达到信息速率的超加和性。我们针对纯状态经典量子通道研究了这种现象，并提供了CN / N的下界，即当JDR被限制为在不超过N个量子通道输出上进行联合测量时，最大信息速率，同时允许任意经典误差更正。当采用级联编码方案，并且内部解码器被迫对N长度做出硬性决定时，我们还显示了超可加性现象的出现-在数学上类似于上述问题-在经典离散无记忆通道的通道容量中内部代码字。利用这种对应关系，我们为以上两个超加和概念开发了一个统一的框架，并表明对于我们的CN / N的下限等于各个通道的渐近容量C的给定分数，N必须与V / C2，其中V是相应的信道分散量。

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