Quantum-access uniformity testing of distributions

Determine the sample/query complexity of uniformity testing in the quantum access model, where one receives quantum states whose amplitude squares equal the target distribution, and establish whether there exist optimal testers or lower bounds for deciding uniformity versus ε‑far from uniform.

Background

The authors discuss classical uniformity testing and its quantum variants. While fully quantum state‑identity testing has seen progress, the distribution‑uniformity problem in the quantum access model remains unresolved.

In the quantum access model, the tester obtains states whose amplitudes correspond to probabilities of an underlying distribution, and the open problem is to characterize the complexity of testing uniformity in this setting.