Entanglement generation in the driven-dissipative Ising model

Quantum entanglement is a resource for quantum information processing. However, generating many-body entangled states robustly is hard. Driven-dissipative platforms can be used to generate these states in the non-equilibrium steady state. In this talk, we discuss various entanglement features of the driven-dissipative Ising model, a descendant of the paradigmatic open Dicke model. Using an exact formalism as well as numerical simulation, we identify the von Neumann entropy, logarithmic negativity, and the quantum Fisher information all throughout the phase diagram. We find that the von Neumann entropy diverges logarithmically with the system size at the phase transition, while the logarithmic negativity remains constant. For the quantum Fisher information, we show that the optimal direction of the spin operator at criticality is determined exactly by the soft mode, and is given exactly by F = 2N for a system size N. This integer value suggests that the steady state at criticality is a product of 2-particle GHZ states in the basis of the soft mode operator. Finally we show that, within the ordered phase and for relatively small dissipation, the quantum Fisher information grows beyond this bound, indicating that the system becomes highly entangled.