  Existence of Anderson localization is considered a manifestation of coherence
of classical and quantum waves in disordered systems. Signatures of
localization have been observed in condensed matter and cold atomic systems
where the coupling to the environment can be significantly suppressed but not
eliminated. In this work we explore the phenomena of localization in random
Lindbladian dynamics describing open quantum systems. We propose a model of
one-dimensional chain of non-interacting, spinless fermions coupled to a local
ensemble of baths. The jump operator mediating the interaction with the bath
linked to each site has a power-law tail with an exponent $p$. We show that the
steady state of the system undergoes a localization entanglement phase
transition by tuning $p$ which remains stable in the presence of coherent
hopping. Unlike the entanglement transition in the quantum trajectories of open
systems, this transition is exhibited by the averaged steady state density
matrix of the Lindbladian. The steady state in the localized phase is
characterised by a heterogeneity in local population imbalance, while the jump
operators exhibit a constant participation ratio of the sites they affect. Our
work provides a novel realisation of localization physics in open quantum
systems.
