Local unitary invariants for multipartite states

Abstract

We study the invariants of arbitrary dimensional multipartite quantum states under local unitary transformations. For multipartite pure states, we give a set of invariants in terms of singular values of coefficient matrices. For multipartite mixed states, we propose a set of invariants in terms of the trace of coefficient matrices. For full ranked mixed states with nondegenerate eigenvalues, this set of invariants is also the necessary and sufficient conditions for the local unitary equivalence of such two states.

8 pages

References in corpus (3)

• Classification of GHZ-type, W-type and GHZ-W-type multiqubit entanglements
• Local Unitary Equivalence of Arbitrary Dimensional Bipartite Mixed Quantum States
• Local unitary equivalent consistence for n-party states and their (n-1)-party reduced density matrices

Cited by in corpus (5)

• Criterion of Local Unitary Equivalence for Multipartite States
• A Complete Set of Invariants for LU-Equivalence of Density Operators
• A Note on Local Unitary Equivalence of Isotropic-like States
• The local unitary equivalence of multipartite pure states
• Local Unitary Invariants for Multipartite Quantum Systems