Heat flow from a measurement apparatus monitoring a dissipative qubit

Abstract

We investigate the heat flow of a qubit coupled to heat baths under continuous quantum measurement. In the steady-state limit, we show that heat always flows from the measurement apparatus into the qubit regardless of the measured qubit state and derive lower and upper bounds for the heat current between the qubit and the measurement apparatus. Furthermore, we study the transient dynamics of the heat current and the excess heat during the transient regime.