How many orthonormal bases are needed to distinguish all pure quantum states?

  • Claudio Carmeli
  • Teiko Heinosaari
  • Jussi Schultz
  • Alessandro Toigo
Topical Review

DOI: 10.1140/epjd/e2015-60230-5

Cite this article as:
Carmeli, C., Heinosaari, T., Schultz, J. et al. Eur. Phys. J. D (2015) 69: 179. doi:10.1140/epjd/e2015-60230-5

Abstract

We collect some recent results that together provide an almost complete answer to the question stated in the title. For the dimension d = 2 the answer is three. For the dimensions d = 3 and d ≥ 5 the answer is four. For the dimension d = 4 the answer is either three or four. Curiously, the exact number in d = 4 seems to be an open problem.

Graphical abstract

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Claudio Carmeli
    • 1
  • Teiko Heinosaari
    • 2
  • Jussi Schultz
    • 2
    • 3
  • Alessandro Toigo
    • 3
    • 4
  1. 1.DIMEUniversità di GenovaSavonaItaly
  2. 2.Turku Centre for Quantum Physics, Department of Physics and AstronomyUniversity of TurkuTurkuFinland
  3. 3.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  4. 4.Sezione di MilanoI.N.F.N.MilanoItaly