Classicalization of Quantum State of Detector by Amplification Process

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.