2006/11/30 by Ulrike Herzog · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Class (philosophy) #Combinatorics #Computer science #Diagonal #Hilbert space #Linear subspace #Mathematics #Operator (biology) #Orthographic projection #Physics #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Quantum optics and atomic interactions #Quantum state #Rank (graph theory) #Representation (politics) #Simple (philosophy) #Unitary state #quant-ph
paper · pdf · doi:10.1103/physreva.75.052309
8 pages, changes in title and presentation
arxiv created 2007/03/12 · openalex publication_date 2007/05/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the measurement for the unambiguous discrimination of two mixed quantum states that are described by density operators \ensuremathρ1 and \ensuremathρ2 of rank d, the supports of which jointly span a 2d-dimensional Hilbert space. Based on two conditions for the optimum measurement operators and on a canonical representation for the density operators of the states, two equations are derived that allow the explicit construction of the optimum measurement, provided that the expression for the fidelity of the states has a specific simple form. For this case, the problem is mathematically equivalent to distinguishing pairs of pure states, even when the density operators are not diagonal in the canonical representation. The equations are applied to the optimum unambiguous discrimination of two mixed states that are similar states, given by \ensuremathρ2=U\ensuremathρ1U^\ifmmode†\else\textdagger\fi, and that belong to the class where the unitary operator U can be decomposed into multiple rotations in the d mutually orthogonal two-dimensional subspaces determined by the canonical representation.