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最小能量时，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通过噪声信道传输经典信息的结论。我们证明，在无辅助协议与私有协议两种情形下，量子信道的容量-功率函数均为凹函数，并进一步证明了对于非纠缠且非相关的输入信号系综具有可加性。这意味着无需采用正则化公式进行求解。我们针对若干标准信道模型，通过数值计算验证了这些性质。对于无噪声信道情形，利用随机量子态的性质与大希尔伯特空间中的集中现象，我们得到了容量-功率函数的解析表达式。