A note on equivalence of bipartite states under local unitary transformations

2005/12/07 by Bao-Zhi Sun, Shao-Ming Fei, Xianqing Li-Jost +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Algebra and Logic #Bipartite graph #Equivalence (formal languages) #Equivalence class (music) #Holomorphic and Operator Theory #Invariant (physics) #Set (abstract data type) #Spectral Theory in Mathematical Physics #Unitary state #Unitary transformation #quant-ph

paper · pdf · doi:10.1088/0305-4470/39/1/l06

published as J. Phys. A: Math. Gen. 39(2006)L43-L47 · 6 pages

openalex publication_date 2005/12/07 · arxiv created 2006/03/11 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The equivalence of arbitrary dimensional bipartite states under local unitary transformations (LUT) is studied. A set of invariants and ancillary invariants under LUT is presented. We show that two states are equivalent under LUT if and only if they have the same values for all of these invariants.

Citations

• Nonlocal Properties of Two-Qubit Gates and Mixed States, and the Optimization of Quantum Computations
• Nonlocal properties and local invariants for bipartite systems
• Concurrence of Arbitrary Dimensional Bipartite Quantum States
• Computing local invariants of quantum-bit systems

Cited by

• Local unitary equivalence of arbitrary dimensional bipartite quantum states