General stabilizer approach for constructing highly entangled graph states

Highly entangled multipartite states such as $k$-uniform ($k$-UNI) and absolutely maximally (AME) serve critical resources in quantum networking other information applications. However, there does not yet exist a complete classification of states, much remains unknown about their entanglement structure. Here we substantially broaden the class known $k$-UNI AME by introducing method for explicitly constructing that combines classical error correcting codes qudit graph states. This fact constitutes general recipe obtaining multipartitite from codes. Furthermore, show at least large subset present, are inequivalent under stochastic local operations communication. is defined an iterative procedure hierarchy