静态经典-量子-纠缠权衡：熵反命题与单字母刻画
Static classical-quantum-entanglement trade-offs: an entropic converse and single-letter characterizations
- School of Electrical and Computer Engineering, Cornell University（康奈尔大学电气与计算机工程学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文给出二分量子态静态容量区域的统一熵反命题，通过支撑超平面刻画容量公式，并针对纯态擦除、对称可扩展态等情形获得完整单字母刻画，揭示非正交丢弃存储器的优势。
AI中文摘要：
二分量子态的直接静态容量区域描述了其渐近转化为经典通信、量子通信和纠缠的过程，所有通信方向均为从Alice到Bob。本文给出了该区域的统一熵反命题。证明同时处理生成和消耗的资源，并针对一个局部仪器推导出全部三个信息不等式。其主要成分包括无信号约束、链式法则、强次可加性以及条件熵的连续性。支撑超平面刻画导出了静态容量公式，这有助于确定容量区域的单字母化。对于纠缠熵为$h$的纯态，在擦除概率为$p$的条件下，完整区域是$0$和$(0,-ph,(1-p)h)$的凸包，再加上单位资源锥。该结论通过使用与早期用于擦除信道动态容量区域的方法相关的子集熵不等式，适用于任意集体仪器。对于对称可扩展态和局部标记的纯态混合，也成立完整的刻画。对于最大相关态，对局部仪器的优化允许精确的矩阵表述和可加的外界。一个明确的量子比特示例表明，非正交的丢弃量子存储器可以胜过所有高效仪器以及所有具有条件交换丢弃态的仪器。对于由Schmidt对齐纯态的量子比特去相位得到的态，存在一个精确阈值，刻画了静态容量公式在任意块长度和正则化后何时为零。对于一般Hadamard态以及去相位态的剩余权衡的完整单字母刻画仍然开放，已识别出充分的可加性条件。
英文摘要：
The direct static capacity region of a bipartite quantum state describes its asymptotic conversion into classical communication, quantum communication, and entanglement, with all communication directed from Alice to Bob. This paper gives a unified entropic converse for this region. The proof treats generated and consumed resources simultaneously and derives all three information inequalities for one local instrument. Its main ingredients are no-signalling, the chain rule, strong subadditivity, and continuity of conditional entropy. A supporting-hyperplane characterization leads to the static capacity formula, which is helpful in determining single-letterization of the capacity region. For a pure state of entanglement entropy $h$ subjected to erasure with probability $p$, the complete region is the convex hull of $0$ and $(0,-ph,(1-p)h)$, plus the unit-resource cone. This statement holds for arbitrary collective instruments by using subset-entropy inequalities related to earlier methods used for the dynamic capacity region of the erasure channel. Complete characterizations also hold for symmetrically extendible states and locally flagged pure-state mixtures. For maximally correlated states, the optimization over local instruments admits an exact matrix formulation and an additive outer bound. An explicit qubit example shows that a nonorthogonal discarded quantum memory can outperform every efficient instrument and every instrument with conditionally commuting discarded states. For states obtained by qubit dephasing of Schmidt-aligned pure states, an exact threshold characterizes when the static capacity formula vanishes, at every blocklength and after regularization. Full single-letter characterizations for general Hadamard states and for the remaining trade-offs for dephased states remain open, with sufficient additivity conditions identified.
