AI 中文总结
该研究针对四体链系统的量子影子反演问题，利用马尔可夫局域性约束，通过引入马尔可夫可实现中心化子，减少了端点后处理带来的模糊性，提升了量子影子反演的可识别性。
AI 中文摘要
我们研究沿链A--B--C--D排列的四体系统在马尔可夫局域性约束下的量子影子反演问题，目标是在不进行完整幺正反演的情况下，重现未知全局幺正作用后固定端点可观测量O_AD的期望值。我们利用马尔可夫容许超映射来构建该任务，并引入马尔可夫可实现中心化子以描述剩余的端点规范自由度。研究表明，无约束的端点后处理范围过宽，因此我们施加端点局域细化条件；在此条件下，每个可实现的端点幺正必须在A|D间分解，因此当完整中心化子包含非乘积幺正时，马尔可夫约束会严格减少中心化子引发的影子模糊性，这为马尔可夫局域性提升量子影子反演可识别性提供了结构机制。
英文摘要
We study quantum shadow inversion under Markovian locality constraints for four-partite systems arranged along the chain $A$--$B$--$C$--$D$. The goal is to reproduce the expectation value of a fixed endpoint observable $O_{AD}$ after an unknown global unitary, without requiring full unitary inversion. We formulate the task using Markov-admissible supermaps and introduce the Markov-implementable centralizer to describe the remaining endpoint gauge freedom. We show that unrestricted endpoint post-processing is too broad, and impose an endpoint-local refinement. Under this condition, every implementable endpoint unitary must factorize across $A|D$, so the Markov constraint strictly reduces the centralizer-induced shadow ambiguity whenever the full centralizer contains non-product unitaries. This provides a structural mechanism by which Markov locality enhances identifiability in quantum shadow inversion.
