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

TL;DR

This paper establishes a new lower bound on the number of copies needed for quantum state tomography, showing that at least on the order of rd/epsilon copies are necessary for accurate reconstruction.

Contribution

It provides an improved sample complexity lower bound for quantum state tomography based on fidelity, refining previous bounds in the field.

Findings

Lower bound of Ω(rd/ε) copies for quantum state tomography

Improves upon previous bounds by Haah et al. and Wright

Focuses on fidelity as the measure of closeness

Abstract

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).