2016/05/01 by Naihuan Jing, Min Yang, Hui Zhao · 10 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Bipartite graph #Connection (principal bundle) #Disjoint sets #Equivalence (formal languages) #Equivalence relation #Kronecker delta #Mathematical functions and polynomials #Quantum Information and Cryptography #Unitary matrix #Unitary state #quant-ph
paper · pdf · doi:10.1063/1.4954230
published in Journal of Mathematical Physics 57(6) (American Institute of Physics) · 13 pages
arxiv created 2016/05/01 · openalex publication_date 2016/06/01 · arxiv updated 2016/06/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The correspondence between local unitary equivalence of bipartite quantum states and simultaneous orthogonal equivalence is thoroughly investigated and strengthened. It is proved that local unitary equivalence can be studied through simultaneous similarity under projective orthogonal transformations, and four parametrization independent algorithms are proposed to judge when two density matrices on ℂd1 ⊗ ℂd2 are locally unitary equivalent in connection with trace identities, Kronecker pencils, Albert determinants and Smith normal forms.