Description:
<jats:p>We show that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="normal">&#x03A9;</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>r</mml:mi><mml:mi>d</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:mo>/</mml:mo></mml:mrow><mml:mi>&#x03F5;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> copies of an unknown rank-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>r</mml:mi></mml:math>, dimension-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi></mml:math> quantum mixed state are necessary in order to learn a classical description with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>1</mml:mn><mml:mo>&#x2013;</mml:mo><mml:mi>&#x03F5;</mml:mi></mml:math> 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).</jats:p>