Counterfactual Quantum Sensing: What Interaction-Free Measurement Can and Cannot Buy

This paper investigates the estimation-theoretic value of interaction-free measurement (IFM), a technique where an object's presence is inferred from a photon that, counterfactually, never interacted with it. The author models the Elitzur-Vaidman interferometer and the quantum Zeno interrogator as channel-estimation problems. By calculating the Fisher information for transmissivity and the Chernoff information for hypothesis discrimination, the study compares IFM against standard direct transmission probing to determine if it truly offers 'supersensitivity' or reduced damage to fragile samples.

The study establishes a clear distinction between the two primary uses of IFM:

1. Estimation: For measuring the transmissivity of an object, IFM is strictly inferior to direct probing. Specifically, the Fisher information of the Elitzur-Vaidman interferometer is exactly half that of direct probing. When normalized by the number of photons absorbed by the object, the information gain per unit of damage is identical to direct probing, meaning the interferometer provides no efficiency advantage for this task.

2. Discrimination: The advantage of IFM lies exclusively in discriminating between the presence and absence of an object. In this scenario, the Chernoff information per absorbed photon grows as $N \ln N$ (where $N$ is the number of Zeno cycles). Crucially, this advantage does not require the object to be opaque; it only requires that one of the two hypotheses being tested is the object's absence. When discriminating between two partial transparencies, the advantage vanishes entirely.

The results clarify the limits of quantum metrology, debunking the notion that IFM is universally 'supersensitive.' By identifying that the advantage is tied to the 'null' nature of the experiment (the absence of an object), the paper provides a practical guide for researchers: IFM is a valuable tool for protecting fragile samples when verifying presence, but it is not a superior method for quantitative spectroscopy or measuring transparency.