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arXiv:2601.11551

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

Masoud Gharahi

quant-phSubmitted Dec 9, 2025• Announced Dec 10, 2025• 0 citations
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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.

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https://github.com/mathoud/Flattening

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ℓ\ellℓ-Multiranks of Multipartite Quantum States via Tensor Flattening: A Mathematica Codebase
We present a Mathematica codebase for computing ℓ\ellℓ-multilinear ranks (ℓ\ellℓ-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 ddd. The code automatically generates all required tensor reshapes and outputs the full ℓ\ellℓ-multirank profile, offering a practical tool for characterizing entanglement in high-dimensional multiqudit systems.
We introduce a general framework for detecting genuine multipartite entanglement and non-full-separability in multipartite quantum systems of arbitrary dimensions based on correlation tensors. Regarding genuine multipartite entanglement, our conditions are comparable to those of previous approaches in the case of qubits, while they show particular strength in the relatively unexplored case of higher-dimensional systems. In the case of non-full-separability, our conditions prove to be advantageous in situations where more than two-body correlations are relevant, where most previous conditions turned out to be weak. Moreover, they allow for the detection of fully bound entangled states. Finally, we also discuss experimentally friendly ways of implementing our conditions, which are based on directly measurable quantities.
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