AI 中文总结
该论文刻画了封闭设备中重复使用固定量子信道所需的浴资源，证明了可达区域由熵交换和参考扩展代价决定，并给出了最小维度速率。
AI 中文摘要
我们刻画了在封闭设备中重复使用固定有限维量子信道所需的浴资源。对于每个时间范围 $T$，一个浴、一个初始状态和一个重复酉操作在用户面前固定。每个输出在下一个输入到达之前返回；没有重置、丢弃、新鲜辅助比特或未计数的控制器可用。近似误差必须对具有量子存储和参考的任意自适应用户消失。记 $r=\lim \log_2(R_T)/T$ 为浴维度速率，$s=\lim S(\omega_T)/T$ 为实际初始熵速率，我们证明可达区域恰好是 $s\ge 0$，$r+s\ge h$ 和 $r-s\ge\kappa$。这里 $h$ 是最大熵交换，$\kappa$ 是平滑的独立参考扩展代价，其中零误差极限在满秩输入的上确界之前取。其精确的固定输入形式是零泄漏量子隐私漏斗的仿射变换。最小维度速率是 $(h+\kappa)/2$。证明结合了熵逆、浴维度无关的支持修复，以及仅编码器的全量子 Slepian–Wolf 回收的封闭自适应实现。所有种子、时钟、工作空间和保留的残差都被计入。工作示例包括去相位、纯替换和一个具有 $0<\kappa<h$ 的量子比特信道。不声称 $\kappa$ 的可计算性或高效电路综合。
英文摘要
We characterize the bath resources needed to supply repeated uses of a fixed finite-dimensional quantum channel in a closed device. For each horizon $T$, one bath, one initial state and one repeated unitary are fixed before the user. Each output is returned before the next input arrives; no reset, discard, fresh ancilla or uncounted controller is available. Approximation error must vanish against arbitrary adaptive users with quantum memory and references. Writing $r=\lim \log_2(R_T)/T$ for the bath dimension rate and $s=\lim S(ω_T)/T$ for the actual initial entropy rate, we prove that the achievable region is exactly $s\ge 0$, $r+s\ge h$ and $r-s\geκ$. Here $h$ is maximum entropy exchange and $κ$ is a smoothed independent-reference extension cost, with the zero-error limit taken before the supremum over full-rank inputs. Its exact fixed-input form is an affine transform of the zero-leakage quantum privacy funnel. The minimum dimension rate is $(h+κ)/2$. The proof combines entropy converses, a bath-dimension-independent support repair, and a closed adaptive implementation of encoder-only fully quantum Slepian--Wolf recycling. All seeds, clocks, workspace and retained residues are counted. Worked examples include dephasing, pure replacement and a qubit channel with $0<κ<h$. No computability of $κ$ or efficient circuit synthesis is claimed.
Comments29 pages; includes two appendices and reproducibility documentation. Code and verification materials: https://github.com/Apsiape/closed-quantum-process-memory-paper
