Abstract

The generation of entanglement in mixed states is salient for 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. For a Markovian environment, evolution of the system density matrix is described by a Lindbladian superoperator. I will discuss two classes of Lindbladian models for open quantum systems. The first one involves disordered, long-range jump operators with a quadratic Lindbladian. I will show that this system undergoes a volume-to-area law entanglement phase transition in the mixed steady state, as a consequence of localization tuned by the range of the jump-operators. The weakly-entangled localized phase exhibits heterogeneity and remains stable in the presence of coherent hopping.

In the second class of models, I will demonstrate the robustness of dynamical aspects of 𝑍2 × 𝑍2 symmetry-protected topological (SPT) order against a wide class of dissipation channels with strong and weak symmetries. The strong symmetries host a decoherence-free steady-state subspace consisting of two delocalized logical qubits. Contrastingly, the localized edge qubits correspond to weak symmetries and thus retain memory of their initial state in the quantum trajectories which can be unravelled via continuous monitoring. I will discuss the potential for dynamically stabilizing entangled states and memory in experiments with dissipative synthetic quantum matter.