Generating Entangled Steady States in Multistable Open Quantum Systems via Initial State Control

Entanglement is a key resource for quantum technologies, yet it is typically fragile and destroyed by dissipation. Paradoxically, engineered dissipation can instead be used to create and stabilize entangled steady states. A major challenge arises in open quantum systems that exhibit multiple steady states, where the long-time behavior depends nontrivially on the initial state. In this talk, I present an analytical framework that predicts the steady state of a system evolving under a Lindblad master equation directly from its initial conditions, without integrating the dynamics. We show that while the steady-state manifold is determined by the kernel of the Liouvillian, the weights within this manifold depend on both the Liouvillian structure and the initial state. We identify a special class of Liouvillians for which the steady state depends solely on the initial overlap with the kernel, greatly facilitating the derivation of analytical expressions for the steady state. As an application, we propose protocols to generate metrologically useful entangled steady states in spin ensembles using balanced collective decay.