Entanglement transition and heterogeneity in long-range quadratic Lindbladians

The generation of entanglement in mixed states is relevant to quantum systems coupled to an environment. The dissipative and mixing properties of the environment are unavoidable in physical platforms for quantum simulation and information processing, where entanglement can be a vital resource. In this work, we explore entanglement and heterogeneity in random Lindbladian dynamics describing open quantum systems. We propose a model of a one-dimensional chain of noninteracting, 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 system undergoes volume -to -area law entanglement phase transition in the mixed steady state by tuning p which remains stable in the presence of coherent hopping. Unlike the entanglement transition in the pure -state quantum trajectories of open systems, this transition is exhibited by the averaged steady-state density matrix of the Lindbladian. The steady state in the area -law phase is characterized by a spatial heterogeneity in local population imbalance, while the jump operators exhibit a constant participation ratio of the sites they affect. Our work provides a theoretical description of an entanglement transition realized in long -ranged open quantum systems and provides an avenue to stabilize quantum correlations in mixed states.