Quantum measurement and the quantum to classical transition in a non-linear quantum oscillator

We study a non-linear quantum mechanical oscillator, acting as a measurement device. Candidate systems for realising such apparatus range from superconducting devices through to nano-mechanical resonators. The measurement device comprises an oscillator circuit where the dynamics of expectation values, in its correspondence limit, are either chaotic-like or periodic depending on the measured state of the quantum object – in this case a qubit. In a previous work we showed how the classical like trajectories of such a quantum system can act as a model of a projective measurement process. Here we investigate the quantum to classical transition of the measurement device and postulate criteria for realisation of an effective implementation of such a device.