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：本文探讨了开发在任何测量序列过程中均保持有效性的量子态层析（QST）方法的问题。具体而言，旨在随着数据的逐步获取，对当前状态估计相关的不确定性进行严格量化。为此，所提出的框架通过将当前状态点估计与置信集合相关联（这些集合能以用户定义的概率保证包含真实量子态），对现有QST技术进行了扩展。该方法基于近期在随时有效置信序列方面的统计学进展。数值结果验证了所提出的随时有效QST的理论覆盖特性。