On Interchangeability of Probe–Object Roles in Quantum–Quantum Interaction-Free Measurement

We examine Interaction-free measurement (IFM) where both the probe and the object are quantum particles. We argue that in this case the description of measurement must be symmetrical with respect to the interchange of the roles of probe and object. A thought experiment is being suggested that helps to determine what does and what doesn’t happen to the state of the particles during the process of non-interaction. It becomes evident that unlike the case of classical object, here the state of both the probe and the object must change. A possible explanation of this might be that the probe and the object form an entangled pair as a result of non-interaction. In other words, we look at the case of two qubits whose degrees of freedom are coupled through a potential interaction (i.e. some potentially observable event happens if the state is │1〉│1〉or │0〉│0〉, but doesn't happen if the state is │1〉│0〉or │0〉│1〉). We show that in the case when they could have interacted, but due to degree-of-freedom mismatch (i.e. state │1〉│0〉) did not, the state of both of them still must chage. The change being creation of entanglement.
S. Filatov, M. Auzinsh, Found. Phys. 49 (3), 283-297, (2019), https://doi.org/10.1007/s10701-019-00244-4