Pauli-resolved virtual distillation

Learning the full Pauli profile of the virtually distilled quantum state $ρ^m/\text{tr}(ρ^m)$ has so far required exponentially many copies of $ρ$. We show that all $4^n$ squared Pauli moments $[\text{tr}(Pρ^m)]^2$ can be learned to additive error $\varepsilon$ with confidence $1-δ$ from one $2m$-re