Biological information processing is generally assumed to be classical. Measured cellular energy budgets of both prokaryotes and eukaryotes, however, fall orders of magnitude short of the power required to maintain classical states of protein conformation and localization at the Å, fs scales predicted by single-molecule decoherence calculations and assumed by classical molecular dynamics models. We suggest that decoherence is limited to the immediate surroundings of the cell membrane and of intercompartmental boundaries within the cell, and that bulk cellular biochemistry implements quantum information processing. Detection of Bell-inequality violations in responses to perturbation of recently-separated sister cells would provide a sensitive test of this prediction. If it is correct, modeling both intra- and intercellular communication requires quantum theory. Copyright © 2021 Elsevier B.V. All rights reserved.