In this letter, we address the problem of developing quantum state tomography (QST) methods that remain valid at any time during a sequence of measurements. Specifically, the aim is to provide a rigorous quantification of the uncertainty associated with the current state estimate as data are acquired incrementally. To this end, the proposed framework augments existing QST techniques by associating current point estimates of the state with confidence sets that are guaranteed to contain the true quantum state with a user-defined probability. The methodology is grounded in recent statistical advances in anytime-valid confidence sequences. Numerical results confirm the theoretical coverage properties of the proposed anytime-valid QST.

翻译：在本通信中，我们解决了开发在测量序列中任意时刻均保持有效的量子态层析成像方法的问题。具体而言，其目标是在数据增量获取过程中，对当前状态估计值的不确定性提供严格的量化。为此，所提出的框架通过将当前的状态点估计与置信集相关联，对现有量子态层析成像技术进行了增强，这些置信集以保证包含用户定义概率下的真实量子态。该方法基于置信序列任意时间有效性方面的最新统计学进展。数值结果证实了所提出的任意时间有效量子态层析成像的理论覆盖特性。