Is the dynamical quantum Cheshire cat detectable?

Abstract

We explore how one might detect the dynamical quantum Cheshire cat proposed by Aharonov et al We show that, in practice, we need to bias the initial state by adding/subtracting a small probability amplitude (‘field’) of the orthogonal state, which travels with the disembodied property, to make the effect detectable (i.e. if our initial state is $\left| \uparrow_z \right\rangle$ , we need to bias this with some small amount δ of state $\left| \downarrow_z \right\rangle$ ). This biasing, which can be done either directly or via weakly entangling the state with a pointer, effectively provides a phase reference with which we can measure the evolution of the state. The outcome can then be measured as a small probability difference in detections in a mutually unbiased basis, proportional to this biasing δ . We show this is different from counterfactual communication, which provably does not require any probe field to travel between sender Bob and receiver Alice for communication. We further suggest an optical polarisation experiment where these phenomena might be demonstrated in a laboratory.

Keywords

• dynamical
• Cheshire cat
• counterfactual communication
• foundations
• weak values