Two Quantum Entangled Cheshire Cats

Quantum entanglement serves as an important resource for quantum processing. In the original thought experiment of the Quantum Cheshire Cat, the physical properties of the cat (state) can be decoupled from its quantum entities. How do quantum entanglement and weak values affect such thought experiment? Here, we conceive a new thought experiment that exploits quantum entanglement with weak (value) measurement. Specifically, we ask: can two entangled particles exchange physical and quantum properties? We answer the question in the affirmative.