Reservoir-engineered high-dimensional entanglement

Quantum reservoir engineering has emerged as a powerful approach for quantum state stabilization and autonomous error correction. However, its prospects in terms of achieving scalable higher-dimensional entanglement remain largely unexplored. In this talk, we will present a stabilization protocol for an Absolutely Maximally Entangled (AME) state in a system of two qudits, parametrically coupled to a lossy cavity acting as an engineered bath. We will first show how the protocol ensures the emergence of the AME state as the unique dark state of driven-dissipative dynamics, using only linear scaling of resources with system size. Next, we will present an analytical approach, based on generalization of projection operator techniques, that extends reservoir engineering schemes to coarse-grained tensor sum spaces. We will then discuss analytical studies of scaling of state fidelity and preparation time with qudit dimension, and benchmark them against numerical predictions accounting for experimental constraints.