No energy transport without discord

We show that without quantum correlations, energy cannot flow. The result follows from a simple theorem that shows that systems whose dynamics do not generate quantum discord are effectively non-interacting. We show that the rate of heat transfer between two quantum systems at different temperatures is directly proportional to the instantaneous rate of increase of diagonal/energetic discord between the systems. Consequently, nanoscale heat transfer experiments can be used to measure discord directly. We report the results of a measurement of the increase in discord due to nanoscale heat flow across an aluminum-sapphire interface and find it to be $4.28 \times 10^{24}$ ${\rm bits}\,{\rm m^{-2}}\,{\rm K^{-1}}\,{\rm s^{-1}}$.