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：本文刻画了当传输信号必须同时携带有最低能量时，通过量子信道传输信息的最优速率。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通过噪声信道传输经典信息的结果。我们证明，对于无辅助和私有协议两种情形，量子信道的容量-功率函数是凹函数，并证明了对于非纠缠且不相关的输入信号系综具有可加性。这意味着我们无需使用正则化公式进行计算。我们针对一些标准信道模型通过数值方法演示了这些性质。利用随机量子态的性质和大希尔伯特空间中的集中现象，我们获得了无噪声信道情况下容量-功率函数的解析表达式。