2008/03/31 by M. Kleinmann, Matthias Kleinmann, Hermann Kampermann +3 · 16 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Combinatorics #Current (fluid) #Mathematics #Operator (biology) #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Quantum state #Rank (graph theory) #State (computer science) #Statistical physics #quant-ph
paper · pdf · doi:10.1063/1.3298683
published in Journal of Mathematical Physics 51(3) (American Institute of Physics) · 33 pages, 3 figures, minor corrections
arxiv created 2009/04/07 · openalex publication_date 2010/03/01 · arxiv updated 2010/03/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We analyze the optimal unambiguous discrimination of two arbitrary mixed quantum states. We show that the optimal measurement is unique and we present this optimal measurement for the case where the rank of the density operator of one of the states is at most 2 (“solution in four dimensions”). The solution is illustrated by some examples. The optimality conditions proven by Eldar et al. [Phys. Rev. A 69, 062318 (2004)] are simplified to an operational form. As an application we present optimality conditions for the measurement, when only one of the two states is detected. The current status of optimal unambiguous state discrimination is summarized via a general strategy.