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ℓ-Multiranks of Multipartite Quantum States via Tensor Flattening: A Mathematica Codebase

Abstract

We present a Mathematica codebase for computing ℓ-multilinear ranks (ℓ-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 ℓ-multirank profile, offering a practical tool for characterizing entanglement in high-dimensional multiqudit systems.

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