Classification of Arbitrary Multipartite Entangled States under Local Unitary Equivalence

Abstract

We propose a practical method for finding the canonical forms of arbitrary dimensional multipartite entangled states, either pure or mixed. By extending the technique developed in one of our recent works, the canonical forms for the mixed $N$-partite entangled states are constructed where they have inherited local unitary symmetries from their corresponding $N+1$ pure state counterparts. A systematic scheme to express the local symmetries of the canonical form is also presented, which provides a feasible way of verifying the local unitary equivalence for two multipartite entangled states.

22 pages; published in J. Phys. A: Math. Theor

References in corpus (4)

• Local Unitary Classification of Arbitrary Dimensional Multipartite Pure States
• Complete set of operational measures for the characterization of 3-qubit entanglement
• Geometric local invariants and pure three-qubit states
• Local unitary equivalent consistence for n-party states and their (n-1)-party reduced density matrices

Cited by in corpus (15)

• Local Unitary Classification of Arbitrary Dimensional Multipartite Pure States
• Local Unitary Equivalence of Multi-qubit Mixed quantum States
• Local Unitary Invariants of Generic Multi-qubit States
• On Local Unitary Equivalence of Two and Three-qubit States
• Quantum State Concentration and Classification of Multipartite Entanglement
• A Complete Set of Invariants for LU-Equivalence of Density Operators
• Local unitary equivalence of generic multi-qubits based on the CP decomposition
• Higher order singular value decomposition and the reduced density matrices of three qubits
• More Communication with Less Entanglement
• Qubits as Hypermatrices and Entanglement
• Local unitary equivalence of arbitrary-dimensional multipartite quantum states
• Local Unitary Invariants for Multipartite Quantum Systems
• Special core tensors of multi-qubit states and the concurrency of three lines
• Local Unitary Equivalence of Tripartite Quantum States In Terms of Trace Identities
• Identifying local unitary equivalence based on reduction of quantum states