Abstract
Now that we have all the notions we need to understand an amplifier operating in the quantum limit, we were able to tackle the relationship between amplification and measurement in the fifth lesson. We began by explaining the distinction between the measurement of a set of very numerous systems, each very weakly coupled to the measuring device, such as nuclear spins, and that of a single system coupled to a so-called pointer system. In the first case, the feedback action of the measuring system on each of the systems is very weak, but is associated with the impossibility of controlling the latter. In the second case, which is the focus of the lecture, the measurement begins with the entanglement between the measured system and the pointer. For superconducting quantum bits, the pointer is the field in the superconducting cavity coupled to the quantum bit. Classically, the pointer would be the Fresnel vector describing the evolution of the field amplitude over time. Quantically, the pointer is a coherent state whose phase depends on the state of the quantum bit. The initial entanglement step therefore corresponds to the formation of a " Schrödinger cat " state involving two coherent states of the cavity field, whose distance in the Fresnel plane is several photons. The second step transforms the pointer into a propagative field which is sent to the amplifier.
