Heat transport through a two-level system under continuous quantum measurement

We study the backaction of quantum measurements on heat transport through a two-level system by consid-ering the continuous quantum measurement onto an eigenstate of the two-level system. For the nonselective measurement, the backaction appears as a dephasing effect on the two-level system. We formulate the heat current under the selective measurement with a stochastic master equation and show that the cross-correlation between the measurement outcomes and the heat current contains information on the backaction. We expect that our findings can be verified by using a platform of superconducting circuits.