Anytime-Valid Quantum State Tomography via Confidence Sequences

TL;DR

This paper introduces a new quantum state tomography method that provides valid uncertainty quantification at any measurement time using confidence sequences, ensuring reliable state estimates during data collection.

Contribution

It extends existing QST techniques by integrating confidence sequences for real-time, rigorous uncertainty quantification during quantum measurements.

Findings

Numerical results confirm the coverage properties of the confidence sequences.

The method guarantees true state containment with user-defined probability at any measurement time.

Abstract

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.