Pauli Measurements Are Near-Optimal for Pure State Tomography

Sabee Grewal, Meghal Gupta, William He, Aniruddha Sen, Mihir Singhal (Jan 09 2026).

Abstract: We give an algorithm for pure state tomography with near-optimal copy complexity using single-qubit measurements. Specifically, given $\widetilde{O}(2^n/\epsilon)$ copies of an unknown pure $n$-qubit state $\lvert\psi\rangle$, the algorithm performs only \textitnonadaptive Pauli measurements, runs in time $\mathrm{poly}(2^n,1/\epsilon)$, and outputs $\lvert \widehat{\psi} \rangle$ that has fidelity $1-\epsilon$ with $\lvert \psi \rangle$ with high probability. This improves upon the previous best copy complexity bound of $\widetilde{O}(3^n/\epsilon)$.

Arxiv: https://arxiv.org/abs/2601.04444