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

Quantum 7, 890 (2023).

https://doi.org/10.22331/q-2023-01-03-890

We show that $Omega(rd/epsilon)$ 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).