Quantum Information Processing

, Volume 11, Issue 6, pp 1751–1763 | Cite as

Quantum measurements on finite dimensional systems: relabeling and mixing

  • Erkka Haapasalo
  • Teiko HeinosaariEmail author
  • Juha-Pekka Pellonpää


Quantum measurements are mathematically described by positive operator valued measures (POVMs). Concentrating on finite dimensional systems, we show that one can limit to extremal rank-1 POVMs if two simple procedures of mixing and relabeling are permitted. We demonstrate that any finite outcome POVM can be obtained from extremal rank-1 POVMs with these two procedures. In particular, extremal POVMs with higher rank are just relabelings of extremal rank-1 POVMs and their structure is therefore clarified.


Quantum measurement POVM Relabeling Mixing 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Erkka Haapasalo
    • 1
  • Teiko Heinosaari
    • 1
    Email author
  • Juha-Pekka Pellonpää
    • 1
  1. 1.Department of Physics and Astronomy, Turku Centre for Quantum PhysicsUniversity of TurkuTurkuFinland

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