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

TL;DR

This paper introduces a Mathematica codebase that efficiently computes $ ext{l}$-multiranks of multiqudit quantum states via tensor flattening, aiding in the detection and characterization of genuine multipartite entanglement in high-dimensional systems.

Contribution

The paper provides a practical computational tool for calculating $ ext{l}$-multiranks using tensor-flattening, enabling improved entanglement detection in complex quantum states.

Findings

Efficient computation of $ ext{l}$-multiranks for multiqudit states.

Automatic generation of tensor reshapes for entanglement analysis.

Practical tool for high-dimensional quantum entanglement characterization.

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.