Consistent approach for quantum measurement

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 detail 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 decouples 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 a Shmidt decomposition with respect to the preferred basis.