可分态违反互补量子关联猜想
When Complementary Measurements Count the Same Classical Bit Twice: Counterexamples to CQC, ECQC, and Complementarity-Based Certification
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中文总结 AI 辅助
该研究针对所有局域维度d≥3，用显式秩-2可分态否定互补量子关联猜想，发现效应源于经典潜变量的互补读出，无需纠缠或量子失谐。
中文摘要 AI 辅助
在互补局域基下测量的关联可作为二分量子态总关联的实验可及探针。互补量子关联猜想断言，两个此类经典互信息的和绝不超过测量前的量子互信息。我们利用一个显式的秩-2可分态，在所有局域维度d≥3下否定了该猜想。两个互补测量中的一个可恢复完整的1比特分支标签，另一个则保留额外的经典关联。对于qutrit（三能级量子系统），超出量恰好为(1/3)log₂(3456/3125)=0.0484156759…比特。连续性可导出满秩可分态的违反情况，因此该效应既不需要纠缠也不需要量子失谐，它源于同一经典潜变量的两个互补读出。
英文摘要
Mutually unbiased measurements are commonly expected to expose independent facets of a quantum state: a correlation that is classical in one basis should disappear in a complementary basis. In higher dimensions, however, this intuition becomes particularly subtle because correlations recovered in different settings need not represent different information. To expose this loophole, we propose a two-branch classical null test: before the setting is chosen, a shared bit selects one of two orthogonal product preparations, producing a rank-two classical--classical state, and the candidate protocol then runs unchanged. Different settings can read the same bit through different outcome patterns. This two-branch classical architecture disproves the complementary-quantum correlation (CQC) conjecture in every dimension $d\geq3$. A distinct rank-two classical--classical state disproves its complete-basis extension (ECQC) at $d=7$, with an overrun that grows without bound along prime dimensions. Its qutrit CQC instance also gives classical false positives for a proposed quantum-correlation measure and a proposed one-sided semi-device-independent steering criterion, and refutes a conditional-probability conjecture. The failures identify the missing requirement: information read in different settings must be nonredundant. In experiments and applications, the same low-overhead architecture can serve as a calibration test before a multibasis score is assigned quantum meaning.
发表机构
- School of Mathematical Sciences, Peking University（北京大学数学科学学院）
- Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
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