Meghal Gupta, William He, Ryan O'Donnell (Jun 16 2025).

Abstract: A fundamental task in quantum information science is \emphstate certification: testing whether a lab-prepared $n$-qubit state is close to a given hypothesis state. In this work, we show that \emphevery pure hypothesis state can be certified using only $O(n^2)$ single-qubit measurements applied to $O(n)$ copies of the lab state. Prior to our work, it was not known whether even sub-exponentially many single-qubit measurements could suffice to certify arbitrary states. This resolves the main open question of Huang, Preskill, and Soleimanifar (FOCS 2024, QIP 2024).

Arxiv: https://arxiv.org/abs/2506.11355