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Spin measurement is studied as a unitary time evolution of the spin coupledto an environment representing the meter and the apparatus. Modelling theenvironment as a heat bath comprising only a finite number of boson modes andrepresented in a basis of coherent states, following the Davydov ansatz, it canbe fully included in the quantum time evolution of the total system. We performnumerical simulations of projective measurements of the polarization, with thespins prepared initially in a neutral pure state. The likewise pure initialstate of the environment is constructed as a product of coherent states of theboson modes with a random distribution of their centroids around the origin ofphase space. Switching the self-energy of the spin and the coupling to the heatbath on and off by a time-dependent modulation, we observe the outcome of themeasurement in terms of the long-time behaviour of the spin. Interacting withthe heat bath, the spins get entangled with it and lose coherence, thusreproduce the "collapse of the wavefunction". The expected quantum randomnessin the final state is manifest in our simulations as a tendency of the spin toapproach either one of the two eigenstates of the measured spin operator,recovering an almost pure state. The unitary time evolution allows us toreproducibly relate these random final states to the respective initial statesof the environment and to monitor the exchange of information between the twosubsystems in terms of their purity and mutual entropy.

Simulating spin measurement with a finite heat bath model for the environment