Sequential Strong Measurements and Heat Vision

TL;DR

The paper investigates how repeated non-demolition measurements can extract infinite information from quantum states and introduces the phenomenon of 'Heat Vision,' where system energy increases indefinitely in certain infinite-dimensional systems due to measurement-induced perturbations.

Contribution

It demonstrates the possibility of infinite parameter estimation via repeated measurements and analyzes the conditions leading to unbounded energy increase, termed 'Heat Vision,' in quantum systems.

Findings

Repeated measurements enable infinite parameter estimation.

Heat Vision causes unbounded energy increase in some systems.

Finite-dimensional systems do not exhibit unbounded perturbations.

Abstract

We study scenarios where a finite set of non-demolition von-Neumann measurements are available. We note that, in some situations, repeated application of such measurements allows estimating an infinite number of parameters of the initial quantum state, and illustrate the point with a physical example. We then move on to study how the system under observation is perturbed after several rounds of projective measurements. While in the finite dimensional case the effect of this perturbation always saturates, there are some 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.