Spin measurement is studied as a unitary time evolution of the spin coupled to an environment representing the meter and the apparatus. Modeling the environment as a heat bath comprising only a finite number of boson modes and represented in a basis of coherent states, following the Davydov ansatz, it can be fully included in the quantum time evolution of the total system. We perform numerical simulations of projective measurements of the polarization, with the spins prepared initially in a neutral pure state. The likewise pure initial state of the environment is constructed as a product of coherent states of the boson modes with a random distribution of their centroids around the origin of phase space. Switching the self-energy of the spin and the coupling to the heat bath on and off by a time-dependent modulation, we observe the outcome of the measurement in terms of the long-time behavior of the spin. Interacting with the heat bath, the spins get entangled with it and lose coherence, thus reproducing the collapse of the wave function. The expected quantum randomness in the final state is manifest in our simulations as a tendency of the spin to approach either one of the two eigenstates of the measured spin operator, recovering an almost pure state. The unitary time evolution allows us to reproducibly relate these random final states to the respective initial states of the environment and to monitor the exchange of information between the two subsystems in terms of their purity and mutual entropy.

• Received 23 April 2022
• Accepted 14 September 2022

DOI:https://doi.org/10.1103/PhysRevA.106.042203