Sequential strong measurements and the heat vision effect

We study the scenarios where a finite set of non-demolition von Neumann measurements is available. We note that, in some situations, the repeated application of such measurements allows estimation of an infinite number of parameters of the initial quantum state, and we illustrate the point with a physical example. We also study how the system under consideration is perturbed after several rounds of projective measurements. While in the finite dimensional case the effect of this perturbation always saturates, there are instances of infinite dimensional systems where such a perturbation is accumulative, and the act of retrieving information about the system increases its energy indefinitely (i.e. we have 'heat vision'). We analyze this effect and discuss a specific physical system with two dichotomic von Neumann measurements where heat vision is expected to show.