Abstract The so-called quantum Cheshire cat is a phenomenon in which an object, identified with a “cat”, is dissociated from a property of the object, identified with the “grin” of the cat. We propose a thought experiment, similar to this phenomenon, with an interferometric setup, where a property (a component of polarization) of an object (photon) can be separated from the object itself and can simultaneously be amplified when it is already decoupled from its object.