Quantum communication holds the potential to revolutionize information transmission by enabling secure data exchange that exceeds the limits of classical systems. One of the key performance metrics in quantum information theory, namely the Holevo bound, quantifies the amount of classical information that can be transmitted reliably over a quantum channel. However, computing and optimizing the Holevo bound remains a challenging task due to its dependence on both the quantum input ensemble and the quantum channel. In order to maximize the Holevo bound, we propose a unified projected gradient ascent algorithm to optimize the quantum channel given a fixed input ensemble. We provide a detailed complexity analysis for the proposed algorithm. Simulation results demonstrate that the proposed quantum channel optimization yields higher Holevo bounds than input ensemble optimization.

翻译：量子通信有望通过实现超越经典系统极限的安全数据交换来革新信息传输。量子信息理论中的关键性能指标——Holevo界，量化了通过量子信道可可靠传输的经典信息量。然而，由于Holevo界同时依赖于量子输入系综和量子信道，其计算与优化仍是一项具有挑战性的任务。为最大化Holevo界，我们提出了一种统一的投影梯度上升算法，用于在固定输入系综条件下优化量子信道。我们对所提算法进行了详细的复杂度分析。仿真结果表明，所提出的量子信道优化方案比输入系综优化能获得更高的Holevo界。