量子比特的互补量子关联具有普适性
Complementary Quantum Correlations Are Universal for Qubits
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中文总结 AI 辅助
该研究证明量子比特可避免互补测量关联的重复计数，建立两量子比特关联受限于测量前量子互信息的定理，可用于获取总关联下界及量子容量下界。
中文摘要 AI 辅助
从量子系统中提取总关联通常需要重构其状态，而许多实验仅能获取少量测量设置。一个可能的捷径是将互补测量得到的互信息相加；然而，在维度高于2的系统中，该过程可能会重复计数同一经典关联。我们证明量子比特可避免此类重复计数：对于任意两量子比特态，在两个互补局域基下观测到的关联受限于测量前的量子互信息。该证明将这种保护归因于Bloch球上的二元熵曲率，并结合了量子比特信息排除权衡与局域退相下的数据处理。因此，两张关联表可给出无需量子态层析的总关联下界；当该值高于1比特时，还可定量证明单向纠缠蒸馏率；将其应用于量子比特信道的Choi态时，相同数据可对该信道的量子容量给出下界。该定理明确了互补性的一种操作用途，以及其关联计数有效的可信二维场景。
英文摘要
Extracting total correlations from a quantum system usually requires reconstructing its state, whereas many experiments access only a few measurement settings. A possible shortcut is to add the mutual informations obtained from complementary measurements; in dimensions above two, however, this procedure can count the same classical correlation twice. We establish that qubits are protected from such overcounting. For every two-qubit state, the correlations observed in two complementary local bases are bounded by the premeasurement quantum mutual information. The proof traces this protection to binary-entropy curvature on the Bloch ball and combines a qubit information-exclusion tradeoff with data processing under local dephasing. Consequently, two correlation tables give a tomography-free lower bound on total correlation. A score above one bit also certifies a quantitative one-way entanglement-distillation rate; when applied to the Choi state of a qubit channel, the same data lower bound its quantum capacity. The theorem therefore identifies both an operational use of complementarity and the trusted two-dimensional setting in which its correlation accounting is valid.
