Effect of Energy Extensivity on the Performance of Open Quantum Interferometers

Studying the performance of a quantum interferometer coupled to an external environment is a problem of conceptual and practical importance. If we consider a quantum interferometer featuring Heisenberg-limited sensitivity, then a typical result is that introducing coupling with the environment degrades the sensitivity to the shot-noise limit. Here we argue that this result crucially depends on whether the interferometer-environment coupling term is subject (or not) to the so-called Kac rescaling that restores extensivity, i.e., whether the coupling Hamiltonian is extensive or not. We present results of the Lindblad equation in the presence and absence of Kac rescaling of the coupling constant. Our results show that for a linear coupling and a harmonic model of the environment, often used in modeling of a quantum interferometer coupled with an environment, the Heisenberg-limited sensitivity may be restored after the Kac rescaling. This result points out the need and the importance to characterize the (model of the) environment of the interferometer at hand.