Hunting for the Quantum Cheshire Cat

We analyze the proposal of Aharonov, Popescu, Rohrlich and Skrzypczyk [New. J. Phys. 15, 113015] of disembodying physical properties from particles. We argue that a different criterion, based on the cross-average $\langle \mathrm{`}cat\ somewhere \mbox{'}\times \mathrm{`}grin\ somewhere\ else\mbox{'}\rangle$ should be used to detect the disembodiment, rather than the local averages $\langle \mathrm{`}cat\ somewhere \mbox{'}\rangle$ and $\langle\mathrm{`}grin\ somewhere\ else\mbox{'}\rangle$. Here, the exact probability distribution and its characteristic function are derived for arbitrary coupling strength, preparation and post-selection. This allows to successfully hunt down the quantum Cheshire cat, showing that it is a consequence of interference, that it is present also for intermediate-strength measurements, and that it is a rather common occurrence in post-selected measurements.