Criterion for SLOCC Equivalence of Multipartite Quantum States

Abstract

We study the stochastic local operation and classical communication (SLOCC) equivalence for arbitrary dimensional multipartite quantum states. For multipartite pure states, we present a necessary and sufficient criterion in terms of their coefficient matrices. This condition can be used to classify some SLOCC equivalent quantum states with coefficient matrices having the same rank. For multipartite mixed state, we provide a necessary and sufficient condition by means of the realignment of matrix. Some detailed examples are given to identify the SLOCC equivalence of multipartite quantum states.

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Cited by in corpus (5)

• Entanglement Classification of Four-partite States under the SLOCC
• Criteria for SLOCC and LU Equivalence of Generic Multi-qudit States
• On construction of finite averaging sets for $SL(2,\mathbb{C})$ via its Cartan decomposition
• Entanglement Classification via Single Entanglement Measure
• Absolutely maximally entangled pure states of multipartite quantum systems