Measuring the heat exchange of a quantum process

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 center of much current attention due to the current control of mesoscopic quantum systems. In this Rapid Communication 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 maybe implemented using ion trap technology. Our scheme should pave the way for experimental explorations of the Landauer principle and hence the intricate energy to information conversion in mesoscopic quantum systems.

Figure 1

The quantum circuit which is used to measure the heat of a quantum process. The ancilla qubit in the upper branch is prepared in a $|+\rangle$ state, the system of interest is prepared in an arbitrary initial state, whereas the reservoir state ${\rho }_R$ defined in the text is a thermal state. First, a controlled operation $v^{†}=e^{i{H}_{R}t}$ is applied on the reservoir, next, the protocol unitary $U$ is applied, and then another controlled operation $v$ is performed on the reservoir and the qubit is measured in the $x\text{−}y$ plane.

Figure 2

Proposal to measure the heat distribution with trapped ions. The level scheme shows the sublevels of ${}^{40}\mathrm{Ca}{}^{+}$ ions for encoding the system and ancilla qubits, along with the required laser fields for the qubit state manipulation, system-reservoir interaction. On the right, two ions in a common harmonic trap are shown along with the different laser beams.