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

We show that $Ω(rd/ε)$ copies of an unknown rank-$r$, dimension-$d$ quantum mixed state are necessary in order to learn a classical description with $1 - ε$ 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).

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