An quantum approach of measurement based on the Zurek's triple model

In a close form without referring the time-dependent Hamiltonian to the total system, a consistent approach for quantum measurement is proposed based on Zurek's triple model of quantum decoherence [W.Zurek, Phys. Rev. D 24, 1516 (1981)]. An exactly-solvable model based on the intracavity system is dealt with in details to demonstrate the central idea in our approach: by peeling off one collective variable of the measuring apparatus from its many degrees of freedom, as the pointer of the apparatus, the collective variable de-couples with the internal environment formed by the effective internal variables, but still interacts with the measured system to form a triple entanglement among the measured system, the pointer and the internal environment. As another mechanism to cause decoherence, the uncertainty of relative phase and its many-particle amplification can be summed up to an ideal entanglement or an Shmidt decomposition with respect to the preferred basis.