We propose and study a toy model for the quantum measurements that yield the
Born's rule of quantum probability. In this model, the electrons interact with
local photon modes and the photon modes are dissipatively coupled with local
photon reservoirs. We treat the interactions of the electrons and photons with
full quantum mechanical description, while the dissipative dynamics of the
photon modes are treated via the Lindblad master equation. By assigning double
quantum dot setup for the electrons coupling with local photons and photonic
reservoirs, we show that the Born's rule of quantum probability can emerge
directly from microscopic quantum dynamics. We further discuss how the
microscopic quantities such as the electron-photon couplings, detuning, and
photon dissipation rate determine the quantum dynamics. Surprisingly, in the
infinite long time measurement limit, the energy conservation already dictates
the emergence of the Born's rule of quantum probability. For finite-time
measurement, the local photon dissipation rate determines the characteristic
time-scale for the completion of the measurement, while other microscopic
quantities affect the measurement dynamics. Therefore, in genuine measurements,
the measured probability is determined by both the local devices and the
quantum mechanical wavefunction.Comment: 8 pages, 4 figure