Anytime-Valid Quantum State Tomography via Confidence Sequences
For quantum information scientists, this provides rigorous uncertainty quantification for state estimates during incremental measurements, addressing a key practical need.
This work develops quantum state tomography methods that provide valid confidence sets at any point during data acquisition, ensuring the true state is contained with user-defined probability. Numerical results confirm theoretical coverage properties.
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.