  It has been shown that a macroscopic system being in a high-temperature
thermal coherent state can be, in principle, driven into a non-classical state
by coupling to a microscopic system. Therefore, thermal coherent states do not
truly represent the classical limit of quantum description. Here, we study the
classical limit of quantum state of a more relevant macroscopic system, namely
the pointer of a detector, after the phase-preserving linear amplification
process. In particular, we examine to what extent it is possible to find the
corresponding amplified state in a superposition state, by coupling the pointer
to a qubit system. We demonstrate quantitatively that the amplification process
is able to produce the classical limit of quantum state of the pointer,
offering a route for a classical state in a sense of not to be projected into a
quantum superposition state.
