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arXiv · 2212.12870

Criteria for SLOCC and LU Equivalence of Generic Multi-qudit States

Jingmei Chang·Naihuan Jing·Tinggui Zhang
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Abstract

In this paper, we study the stochastic local operation and classical communication (SLOCC) and local unitary (LU) equivalence for multi-qudit states by mode-$n$ matricization of the coefficient tensors. We establish a new scheme of using the CANDECOMP/PARAFAC (CP) decomposition of tensors to find necessary and sufficient conditions between the mode-$n$ unfolding and SLOCC\&LU equivalence for pure multi-qudit states. For multipartite mixed states, we present a necessary and sufficient condition for LU equivalence and necessary condition for SLOCC equivalence.

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Jingmei Chang, Naihuan Jing, Tinggui Zhang. 2022-12-25. Criteria for SLOCC and LU Equivalence of Generic Multi-qudit States. https://doi.org/10.1007/s10773-022-05267-8

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