We discuss how quantum jumps affect localized regimes in driven-dissipative disordered many-body systems featuring a localization transition. We introduce a deformation of the Lindblad master equation that interpolates between the standard Lindblad and the no-jump non-Hermitian dynamics of open quantum systems. As a platform, we use a disordered chain of hard-core bosons with nearest-neighbor interactions and subject to incoherent drive and dissipation at alternate sites. We probe both the statistics of complex eigenvalues of the deformed Liouvillian and dynamical observables of physical relevance. We show that reducing the number of quantum jumps, achievable through realistic postselection protocols, can promote the emergence of the localized phase. Our findings are based on exact diagonalization and time-dependent matrix-product state techniques.

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• Dynamical localization
• Dynamical phase transitions
• Nonequilibrium statistical mechanics
• Disordered systems
• Non-Hermitian systems
• Exact diagonalization
• Full counting statistics
• Lindblad equation
• Matrix product states
• Random matrix theory