Post-measurement bipartite entanglement entropy in conformal field theories

We derive exact formulas for bipartite von Neumann entanglement entropy after partial projective local measurement in (1+1) -dimensional conformal field theories with periodic and open boundary conditions. After defining the setup we will check numerically the validity of our results in the case of Klein-Gordon field theory (coupled harmonic oscillators) and spin-1/2 XX chain in a magnetic field. The agreement between analytical results and the numerical calculations is very good. We also find a lower bound for localizable entanglement in coupled harmonic oscillators.