2004/11/30 by Michael Nathanson · 180 citations
Chemistry · Computer Science · Materials Science · Mathematics · Physics and Astronomy · #Algebra over a field #LOCC #Machine Learning in Materials Science #Mathematical physics #Mathematics #Molecular spectroscopy and chirality #Physics #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum mechanics #Quantum state #quant-ph
paper · pdf · doi:10.1063/1.1914731
published in Journal of Mathematical Physics 46(6) (American Institute of Physics) · 22 pages, published version. Some proofs rewritten for clarity
openalex publication_date 2005/05/12 · arxiv created 2005/07/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Two types of results are presented for distinguishing pure bipartite quantum states using local operations and classical communications. We examine sets of states that can be perfectly distinguished, in particular showing that any three orthogonal maximally entangled states in C3⊗C3 form such a set. In cases where orthogonal states cannot be distinguished, we obtain upper bounds for the probability of error using LOCC taken over all sets of k orthogonal states in Cn⊗Cm. In the process of proving these bounds, we identify some sets of orthogonal states for which perfect distinguishability is not possible.