$\ell$-Multiranks of Multipartite Quantum States via Tensor Flattening: A Mathematica Codebase

Abstract

We present a Mathematica codebase for computing $\ell$-multilinear ranks ($\ell$-multiranks) of multiqudit quantum states using tensor-flattening techniques. By calculating the ranks of all bipartition-induced matricizations, the method provides an efficient criterion for detecting Genuine Multipartite Entangled (GME) states in systems with local dimension $d$. The code automatically generates all required tensor reshapes and outputs the full $\ell$-multirank profile, offering a practical tool for characterizing entanglement in high-dimensional multiqudit systems.