An Improved Sample Complexity Lower Bound for (Fidelity) Quantum State Tomography

We show that $\mathrm{\Omega }(rd\mathrm{/}\epsilon )$ copies of an unknown rank-$r$, dimension-$d$ quantum mixed state are necessary in order to learn a classical description with $1-\epsilon$ fidelity. This improves upon the tomography lower bounds obtained by Haah, et al. and Wright (when closeness is measured with respect to the fidelity function).