  A common-sense perception of a physical system is that it is inseparable from
its physical properties. The notion of Quantum Cheshire Cat challenges this, as
far as quantum systems are concerned. It shows that a quantum system can be
decoupled from its physical property under suitable pre and postselections.
However, in the Quantum Cheshire Cat setup, the decoupling is not permanent.
The photon, for example, and its circular polarization is separated and then
recombined. In this paper, we present a thought experiment where we decouple
two photons from their respective polarizations and then interchange them
during recombination. Thus, our proposal shows that the belongingness of a
property for a physical system is very volatile in the quantum world. This
raises the question of reality of an observable at a much deeper level.
