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

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.

References in corpus (7)

• Local Unitary Equivalence of Multi-qubit Mixed quantum States
• Asymptotic properties of entanglement polytopes for large number of qubits
• SLOCC Invariants for Multipartite Mixed States
• On Local Unitary Equivalence of Two and Three-qubit States
• Classification of arbitrary-dimensional multipartite pure states under stochastic local operations and classical communication using the rank of coefficient matrix
• Criterion for SLOCC Equivalence of Multipartite Quantum States
• Local unitary equivalence of generic multi-qubits based on the CP decomposition

Cited by in corpus (2)

• Multipartite entanglement classes of a multiport beam-splitter
• Identifying local unitary equivalence based on reduction of quantum states