Executive Summary : | The aim of this proposal is to study the measurement induced phase transitions (MIPTs) that emerge in many-body quantum systems subject to quantum measurements and collective dissipation. We anticipate that such phases will be characterized by the scaling property and dynamics of entanglement. In particular, we will study the interplay between collective dissipation and MIPTs via numerical and analytical studies of some quantum circuit models as well as those with a given Hamiltonian subject to continuous quantum measurement - namely we will study standard Clifford quantum circuits under collective dephasing, the transverse Ising model subject to continuous quantum measurement and collective dephasing, and MIPTs of collectively emitting ensembles of quantum emitters. |