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Title: Upper bounds on the error probabilities and asymptotic error exponents in quantum multiple state discrimination

We consider the multiple hypothesis testing problem for symmetric quantum state discrimination between r given states σ₁, …, σ{sub r}. By splitting up the overall test into multiple binary tests in various ways we obtain a number of upper bounds on the optimal error probability in terms of the binary error probabilities. These upper bounds allow us to deduce various bounds on the asymptotic error rate, for which it has been hypothesized that it is given by the multi-hypothesis quantum Chernoff bound (or Chernoff divergence) C(σ₁, …, σ{sub r}), as recently introduced by Nussbaum and Szkoła in analogy with Salikhov's classical multi-hypothesis Chernoff bound. This quantity is defined as the minimum of the pairwise binary Chernoff divergences min{sub j
Authors:
 [1] ;  [2] ;  [3] ;  [4]
  1. Department of Mathematics, Royal Holloway University of London, Egham TW20 0EX (United Kingdom)
  2. (Belgium)
  3. Física Teòrica: Informació i Fenomens Quàntics, Universitat Autònoma de Barcelona, ES-08193 Bellaterra, Barcelona (Spain)
  4. (Hungary)
Publication Date:
OSTI Identifier:
22305859
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 10; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; POTENTIALS; PROBABILITY; QUANTUM MECHANICS; QUANTUM STATES; SYMMETRY