Setting bounds on the absorption cross-sections of molecular systems. There has been a long-running controversy regarding the “quantum advantage” for multiphoton excitation of molecules with entangled photons and if quantum multiphoton imaging can be realized. Although theoretical proposals have been advanced for decades, no experimental work (with the exception of a publication by Jeff Kimble’s group in the 1990s) appeared in the literature until 2006 when reports from a small number of groups began to emerge of a large quantum enhancement (e.g. up to 10 orders of magnitude) of the two photon excitation rate using entangled pairs compared to classical light. Last year, a paper describing a microscope based on the “entangled two-photon absorption” (E2PA) effect was published in Journal of the American Chemical Society. On the other hand, it has emerged from discussions at scientific meetings that many researchers have failed to replicate the results in these numerous publications, or to find any other evidence for this enhancement. As a result, there is considerable skepticism of the publications making these remarkable claims. Unfortunately, these negative results haven’t been published and therefore a rigorous basis for resolving the controversy hasn’t yet been established. Finally, new experiments at JILA have finally set upper-bounds for the E2PA cross-sections in molecular fluorophores, including those investigated in previous reports. We performed both classical and quantum light excitation in the same optical transmission and fluorescence-based systems with rigorously characterized states of light and measurement sensitivities. We find that E2PA cross-sections are at least four to five orders of magnitude smaller than previously reported. Our results imply that the signals and images reported in previous publications are artifacts. Although we don’t expect this contribution to be the last word on the subject, this work introduces a new level of experimental rigor that will lead towards new designs for quantum microscopes and sensors.