Local unitary equivalence is central to entanglement quantification and classification. Identifying the local unitary equivalence remains a formidable challenge. We address this problem for a class of quantum states with one highly degenerate eigenvalue and the rest nondegenerate simple eigenvalues that are pivotal to structured resources in quantum resource theory. We introduce a reduction procedure that maps each state to a reduced state by nullifying the highest-multiplicity eigenvalue and prove that the local unitary equivalence of the original states is equivalent to that of their reduced counterparts. For the resulting pure or nondegenerate reduced states, we employ the existing invariants or fixed-point subgroup criteria to establish a complete discrimination framework, although the existing criteria cannot directly identify the local unitary equivalence of the original states. We also verify the local unitary equivalence of two families of single-parametrized multipartite mixed states constructed by perturbing absolutely maximally entangled states from distinct combinatorial origins, demonstrating the efficacy and generality of our approach.

Close

PrevNext

View figure in article

• Quantum information processing
• Quantum information theory