ON the Number of Elements Needed in a POVM Attaining the Accessible Information

  • Peter W. Shor


We investigate an symmetric set of three quantum states in three dimensions with interesting properties, which we call the lifted trine states. We show that for the ensemble consisting of the three lifted trine states taken with equal probabilities, the POVM measurement realizing the accessible information must contain six projectors, giving a counter-example to a conjecture of Levitin.


Quantum measurement accessible information POVM’s 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M. Sasaki, S. M. Barnett, R. Jozsa, M. Osaki and O. Hirota, “Accessible information and optimal strategies for real symmetrical quantum sources,” Phys. Rev. A, vol. 59, 3325–3335, 1999, LANL e-print quant-ph/9812062.CrossRefADSGoogle Scholar
  2. [2]
    C. Fuchs, personal communication.Google Scholar
  3. [3]
    L. B. Levitin, “Optimal quantum measurements for two pure and mixed states,” in Quantum Communications and Measurement (V. P. Belavkin, O. Hirota and R. L. Hudson, eds.), Pfenum Press, New York, 1995, pp. 439–448.Google Scholar
  4. [4]
    A. S. Holevo, “Information-theoretical aspects of quantum measurement,” Problemy Peredachi Informatsii vol. 9, no. 2, pp. 31–42 1973 (in Russian); English translation: A. S. Kholevo, Problems of Information Transmission, vol. 9, pp. 110–118, 1973.zbMATHMathSciNetGoogle Scholar
  5. [5]
    A. Peres and W. K. Wootters, “Optimal detection of quantum information,” Phys. Rev. Lett., vol. 66, pp. 1119–1122 (1991).CrossRefADSGoogle Scholar
  6. [6]
    T.M. Cover and J.A. Thomas, Elementsof InformationTheory, Wiley, New York, 1991.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Peter W. Shor
    • 1
  1. 1.AT&T Labs —ResearchFlorham ParkUSA

Personalised recommendations