Local Unitary Classification of Arbitrary Dimensional Multipartite Pure States

Abstract

We propose a practical entanglement classification scheme for general multipartite pure states in arbitrary dimensions under local unitary equivalence by exploiting the high order singular value decomposition technique and local symmetries of the states. By virtue of this scheme, the method of determining the local unitary equivalence of $n$-qubit states proposed by Kraus is extended to the case for arbitrary dimensional multipartite states.

10 pages; published in Phys. Rev. Lett

References in corpus (7)

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Cited by in corpus (36)

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• Local Unitary Invariants of Generic Multi-qubit States
• Classification of Arbitrary Multipartite Entangled States under Local Unitary Equivalence
• Entanglement Classification of Four-partite States under the SLOCC
• SLOCC Invariants for Multipartite Mixed States
• Qudit Hypergraph States
• Minimal Renyi-Ingarden-Urbanik entropy of multipartite quantum states
• On Local Unitary Equivalence of Two and Three-qubit States
• Limits to multipartite entanglement generation with bosons and fermions
• Quantum State Concentration and Classification of Multipartite Entanglement
• Local unitary equivalence of quantum states and simultaneous orthogonal equivalence
• Bell-type inequality and quantum nonlocality in four-qubit systems
• Local unitary invariants for multipartite states
• A Complete Set of Invariants for LU-Equivalence of Density Operators
• A Note on Local Unitary Equivalence of Isotropic-like States
• Connection between Measurement Disturbance Relation and Multipartite Quantum Correlation
• Local unitary equivalence of generic multi-qubits based on the CP decomposition
• Criteria for SLOCC and LU Equivalence of Generic Multi-qudit States
• Relations among $k$-ME concurrence, negativity, polynomial invariants, and tangle
• Sequential generation of Polynomial Invariants and N-body non-local correlations
• The local unitary equivalence of multipartite pure states
• Higher order singular value decomposition and the reduced density matrices of three qubits
• A Note on State Decomposition Independent Local Invariants
• Qubits as Hypermatrices and Entanglement
• Local unitary equivalence of arbitrary-dimensional multipartite quantum states
• Local Unitary Invariants for Multipartite Quantum Systems
• Layer-by-layer disentangling two-dimensional topological quantum codes
• Identifying local unitary equivalence based on reduction of quantum states
• Special core tensors of multi-qubit states and the concurrency of three lines
• Entanglement in the symmetric subspace: mapping multipartite to bipartite states
• Local Unitary Equivalence of Tripartite Quantum States In Terms of Trace Identities
• Absolutely maximally entangled pure states of multipartite quantum systems