I have been reading and studying this article recently about non-local weak measurements and quantum erasure. Usually the weak measurement formalism is described using the Von Neumann scheme for quantum measurement, which involves a system and a meter, the latter being shifted by an amount depending on the physical state of system and the strength of the interaction. In the case of a strong measurement, this can be seen as a CNOT gate acting on the meter.
I am interested in the optical implementation of such measurements, using two qubits. Usually the CNOT gate is easily implemented using a Polarizing Beam Splitter (PBS), in this case the control qubit is the polarization degree of freedom of a photon and the target qubit is its path degree of freedom after the beamsplitter.
However, I would like to know if it is possible to implement a Von Neumann measurement using the polarization of two different photons, the polarization of the meter photon being shifted according to the polarization of the system photon.
Since two-photon interactions are very hard to get using linear optics, I was thinking about one of the few that I am aware of : a Bell state measurement where one records coincidence counts at the outputs of a beam splitter. According to the Hong-Ou-Mandel effect, only the singlet Bell state would yield such coincidence counts and the measurement would thus be a projection on this state.
Can this be described in term of meter and system qubit, or in term of Von Neumann interaction ? What exactly would be the observable being measured here ?
Thanks.