Emergence of the Born rule in strongly driven dissipative systems

To understand the dynamical origin of the measurement in quantum mechanics, several models have been put forward which have a quantum system coupled to an apparatus. The system and the apparatus evolve in time, and the Born rule for the system to be in various eigenstates of the observable is naturally obtained. In this paper, we show that the effect of the drive-induced dissipation in an open quantum system can lead to the Born rule, even if there is no separate apparatus. The applied drive needs to be much stronger than the system-environment coupling. In this condition, we show that the dynamics of the driven-dissipative system could be reduced to a Milburn-like form, using a recently proposed fluctuation-regulated quantum master equation [A. Chakrabarti and R. Bhattacharyya, Phys. Rev. A 97, 063837 (2018).]. The irreversible part of the dynamics is caused by drive-induced dissipation. The resulting mixed state is identical to that obtained by using the Born rule.