An experimental proposal to study collapse of the wave function in travelling-wave parametric amplifiers

The read-out of a microwave qubit state occurs using an amplification chain that enlarges the quantum state to a signal detectable with a classical measurement apparatus. However, at what point in this process is the quantum state really 'measured'? In order to investigate whether the `measurement' takes place in the amplification chain, in which a parametric amplifier is often chosen as the first amplifier, it is proposed to construct a microwave interferometer that has such an amplifier added to each of its arms. Feeding the interferometer with single photons, the interference visibility depends on the gain of the amplifiers and whether a measurement collapse has taken place during the amplification process. The visibility as given by standard quantum mechanics is calculated as a function of gain, insertion loss and temperature. We find a visibility of 1/3 in the limit of large gain without taking into account losses, which is reduced to 0.26 in case the insertion loss of the amplifiers is 2.2 dB at a temperature of 50 mK. It is shown that if the wave function collapses within the interferometer, the measured visibility is reduced compared to its magnitude predicted by standard quantum mechanics once this collapse process sets in.