2001/12/31 by Ulrike Herzog, János A. Bergou, Janos A. Bergou · 2 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1103/physreva.65.050305
Representation improved and generalized, references added. Accepted as a Rapid Communication in Phys. Rev. A
arxiv created 2002/04/11 · openalex publication_date 2002/05/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A measurement strategy is developed for a different kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given nonorthogonal quantum states occurring with given a priori probabilities. A general analytical solution is obtained for N states that are restricted to a two-dimensional subspace of the Hilbert space of the system. The result for the special case of three arbitrary but linearly dependent states is applied to a variety of sets of three states that are symmetric and equally probable. It is found that, in this case, the minimum-error probability for distinguishing one of the states from the other two is only about half as large as the minimum-error probability for distinguishing all three states individually.