发表机构
University of York（约克大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究确定了纯损耗玻色信道在能量约束下的双向容量公式，并证明其最优性，建立了统一的自适应通信框架。
AI 中文摘要
我们在无条件平均发射光子数约束下，确定了纯损耗玻色信道的双向量子容量、纠缠分发容量、私密容量和秘密密钥容量。对于透射率 $\eta$ 和平均光子数 $N$，这四个容量一致，并由 $g(N)-g((1-\eta)N)$ 给出，其中 $g$ 是热模式的熵。这通过确立2009年引入的反向相干信息率的最优性，解决了长期存在的有限能量容量问题。我们的核心工具是扇区隐形传态模拟，我们专门开发该工具以将输入能量约束转移到共享纠缠资源上，从而在一般自适应协议的逆向论证中保持该约束。对于每个 $N>0$，我们进一步表明相应的强逆阈值与无约束值 $-\log_2(1-\eta)$ 一致。对于具有硬总光子数截断的并行协议，相同的有限能量容量公式反而满足指数强逆。这些结果共同为自适应玻色通信建立了统一的有限能量框架，并揭示了能量约束如何从根本上重塑可达速率和逆向界限。
英文摘要
We determine the two-way quantum, entanglement-distribution, private, and secret-key capacities of the pure-loss bosonic channel under an unconditional mean transmitted-photon-number constraint. For transmissivity $η$ and mean photon number $N$, all four capacities coincide and are given by $g(N)-g((1-η)N)$, where $g$ is the entropy of a thermal mode. This resolves the longstanding energy-constrained capacity problem by establishing the optimality of the reverse-coherent-information rate introduced in 2009. Our central tool is sector teleportation simulation, which we develop specifically to transfer the input-energy constraint to the shared entanglement resource, thereby preserving the constraint throughout converse arguments for general adaptive protocols. For every $N>0$, we further show that the corresponding strong-converse thresholds coincide with the unconstrained value $-\log_2(1-η)$. For parallel protocols with a hard total-photon-number cutoff, the same energy-constrained capacity formula instead satisfies an exponential strong converse. As an extension, we determine the energy-constrained two-way capacities of the quantum-limited amplifier, showing that classical assistance does not improve its unassisted quantum and private rates. Together, these results establish a unified finite-energy framework for adaptive bosonic communication and reveal how energy constraints fundamentally reshape both attainable rates and converse bounds.
CommentsSubmitted version which includes both pure loss and quantum limited amplification. Comments and feedback are welcome
