  Very recently, interferometric methods have been proposed to measure the full
statistics of work performed on a driven quantum system [Dorner et al. Phys.
Rev. Lett. 110 230601 (2013)] and [Mazzola et al. Phys. Rev. Lett. 110 230602
(2013)]. The advantage of such schemes is that they replace the necessity to
make projective measurements by performing phase estimation on an appropriately
coupled ancilla qubit. These proposals are one possible route to the tangible
experimental exploration of quantum thermodynamics, a subject which is the
centre of much current attention due to the current control of mesoscopic
quantum systems. In this Letter we demonstrate that a modification of the phase
estimation protocols can be used in order to measure the heat distribution of a
quantum process. In addition we demonstrate how our scheme may be implemented
using ion trap technology. Our scheme should pave the way for the first
experimental explorations of the Landauer principle and hence the intricate
energy to information conversion in mesoscopic quantum systems.
