发表机构
Perimeter Institute for Theoretical Physics; University of Waterloo; Institute for Quantum Computing, University of Waterloo（Perimeter理论物理研究所; 滑铁卢大学; 滑铁卢大学量子计算研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明完全置换不变性限制量子信道通信优势，使渐近优化简化为单次使用，并建立强逆定理与输出熵界，揭示可加性结果的统一结构。
AI 中文摘要
跨信道使用的相关性可以提高量子通信速率，这使得在任意大的块上进行优化成为确定量子容量中的核心困难。我们证明了完全置换不变性如何限制每个有限维无记忆信道的这种优势。每使用一次的优化相干信息收敛到单次使用的最大值，并因此在有限块长度上达到其上确界。因此，有限块超可加性仍然可能，而渐近优化简化为单次信道使用。我们还为纯源纠缠生成建立了强逆定理，在置换不变输入下：在高于单次使用相干信息最大值的任何固定速率下，保真度趋于零。在这些通信界之外，我们识别出完全有界范数和夹层Rényi信道量（用于对抗替换器和纠缠辅助通信的判别）背后的共同结构。De Finetti约简和置换协变性在共享变分框架内为其已知的乘性和可加性结果提供了系统的替代证明。我们进一步表明，对于置换不变输入，相关性无法使每使用一次的输出熵渐近降低到低于单次使用的最小值。该熵界适用于大于一的Rényi阶和von Neumann熵，将对称性的作用从通信界扩展到输出熵的控制。
英文摘要
Correlations across channel uses can improve quantum communication rates, making optimization over arbitrarily large blocks a central difficulty in determining quantum capacity. We show how full permutation invariance limits this advantage for every finite-dimensional memoryless channel. The optimized coherent information per use converges to the single-use maximum and consequently attains its supremum at a finite block length. Thus finite-block superadditivity remains possible, while the asymptotic optimization reduces to a single channel use. We also establish a strong converse for pure-source entanglement generation with permutation-invariant inputs: at any fixed rate above the single-use coherent-information maximum, the fidelity tends to zero. Beyond these communication bounds, we identify a common structure underlying completely bounded norms and the sandwiched Rényi channel quantities governing discrimination against a replacer and entanglement-assisted communication. De Finetti reduction and permutation covariance yield systematic alternative proofs of their known multiplicativity and additivity results within a shared variational framework. We further show that, for permutation-invariant inputs, correlations cannot sustain an asymptotic reduction in output entropy per use below the single-use minimum. This entropy limit holds for Rényi orders greater than one and for the von Neumann entropy, extending the role of symmetry from communication bounds to the control of output entropy.
