The optimal rate at which information can be sent through a quantum channel when the transmitted signal must simultaneously carry some minimum amount of energy is characterized. To do so, we introduce the quantum-classical analogue of the capacity-power function and generalize results in classical information theory for transmitting classical information through noisy channels. We show that the capacity-power function for a quantum channel, for both unassisted and private protocol, is concave and also prove additivity for unentangled and uncorrelated ensembles of input signals. This implies we do not need regularized formulas for calculation. We numerically demonstrate these properties for some standard channel models. We obtain analytical expressions for the capacity-power function for the case of noiseless channels using properties of random quantum states and concentration phenomenon in large Hilbert spaces.

翻译：随着传输信号必须同时携带一定最小能量时，通过量子信道传输信息的最优速率被刻画。为此，我们引入了容量-功率函数的量子经典类比，并推广了经典信息论中关于噪声信道传输经典信息的结果。我们证明，对于无辅助协议和隐私协议两种情形，量子信道的容量-功率函数具有凹性，并进一步验证了非纠缠且非关联输入信号系综的可加性。这意味着我们无需使用正则化公式进行计算。我们通过数值实验展示了这些性质在若干标准信道模型中的体现。利用随机量子态的性质以及大希尔伯特空间中的集中现象，我们推导了无噪声信道情形下容量-功率函数的解析表达式。