AI 中文总结
该研究建立了量子纠错与量子达尔文主义间的精确权衡关系，证明逻辑保真度超临界阈值会阻碍达尔文主义冗余度出现，首次给出二者的定量信息论联系。
AI 中文摘要
量子纠错（QEC）与量子达尔文主义描述了系统-环境相互作用的对立结果：量子纠错旨在保护逻辑量子信息，而量子达尔文主义则通过经典信息扩散到环境中解释了客观经典信息的出现。尽管二者具有共同的物理起源，但此前尚未建立这些范式之间的直接定量联系。我们引入了一个基于Shor [[9,1,3]]量子纠错码的逻辑GHZ块的可精确求解的块环境模型，该模型与N个环境量子比特集体耦合。针对任意环境规模和不完善的恢复效率，系统地得到了逻辑保真度、Holevo信息和达尔文主义冗余度。消除共同的退相干参数后，得到了达尔文主义冗余度与恢复后逻辑保真度直接相关的精确权衡关系，表明冗余经典记录的出现是以牺牲逻辑量子信息为代价的。我们进一步证明了一个与模型无关的不可行定理，该定理表明，无论微观哈密顿量或环境结构如何，只要逻辑保真度超过临界阈值，就会阻止达尔文主义冗余度的出现。该可求解模型达到了这一通用界限，建立了逻辑量子信息保护与冗余经典记录出现之间的首个定量信息论联系。
英文摘要
Quantum error correction (QEC) and Quantum Darwinism describe opposing consequences of system-environment interactions: QEC seeks to preserve logical quantum information, whereas Quantum Darwinism explains the emergence of objective classical information through its proliferation into the environment. Despite their common physical origin, no direct quantitative connection between these paradigms has previously been established. We introduce an exactly solvable block-environment model based on the logical GHZ block of the Shor [[9,1,3]] quantum error-correcting code, collectively coupled to N environment qubits. The logical fidelity, Holevo information, and Darwinistic redundancy are obtained systematically for arbitrary environment size and imperfect recovery efficiency. Eliminating the common decoherence parameter yields an exact tradeoff relating Darwinistic redundancy directly to the post-recovery logical fidelity, demonstrating that the emergence of redundant classical records occurs at the expense of logical quantum information. We further prove a model-independent no-go theorem showing that the logical fidelity exceeds a critical threshold precludes the emergence of Darwinistic redundancy, irrespective of the microscopic Hamiltonian or environment structure. The solvable model saturates this general bound, establishing the first quantitative information-theoretic connection between logical quantum information protection and the emergence of redundant classical records.
Comments14 pages, 2 figures
