the quasi-orthogonality of the input and output states selected. However, in many applications, limitations are not related to the low intensity of the signal [@hosten2008], but to the smallest change that the detector can measure irrespectively of the intensity level of the signal.

A potential advantage of our approach is that we make use of the concept of trace distance, a clear and direct measure of the degree of distinguishability of two quantum states. Indeed, the trace distance gives us the minimum probability of error of distinguishing two quantum states that can be achieved under the best detection system one can imagine [@helstrom1976]. Measuring tiny quantities is essentially equivalent to distinguishing between nearly parallel quantum states. Therefore we offer a very basic and physical understanding of how WVA works, based on the idea of how WVA transforms very close quantum states, which can be useful to the general physics reader.

Here were we use an approach slightly different from what other analysis of WVA do, where most of the times the tool used to estimate its usefulness is the Fisher information. Contrary to how we use the trace distance here, to set a sensitivity bound only considering how the quantum 