Generalized spectroscopy; coherence, superposition, and loss

We analyze single particle coherence and interference in the presence of particle loss and derive an inequality that relates the preservation of coherence, the creation of superposition with the vacuum, and the degree of particle loss. We find that loss channels constructed using linear optics form a special subclass. We suggests a generalized spectroscopy where, in analogy with the absorption spectrum, we measure a "coherence loss spectrum" and a "superposition creation spectrum". The theory is illustrated with examples.