In this talk, we discuss two ways to realize critical mixed states on a quantum simulator, (i) local dephasing acting on a pure critical ground state (ii) measurement and feedback on a pure critical ground state. Although the states all have power-law correlations, their long-range quantum entanglement shows distinct behaviors, as characterized by different scaling of negativity. I will present two examples obtained by critical Ising and Luttinger liquid ground state and the universality of these mixed states in terms of conformal defects. Finally, we discuss the experimental observation of the mixed-state critical phases.