  The measurement-induced phase transition (MIPT) occurs when the system is
evolving under unitary evolution together with local measurements followed by
post-selection. We propose a generalized version of the Lindblad master
equation as a continuous equation, to describe the dynamics of second R\'enyi
entropy in the MIPT. This generalized Lindblad equation explicitly takes into
account the post-selection in the MIPT, which is realized as the
Einstein-Podolsky-Rosen (EPR) state projection in the equation. Also, this
generalized Lindblad equation preserves the Hermitian, unit trace, and positive
definiteness of the density matrix. We further use the hard-core Bose-Hubbard
model as a concrete example to numerically confirm that our generalized
Lindblad equation is applicable to describing the MIPT.
