Foundations of Physics

, Volume 35, Issue 12, pp 1985–2006 | Cite as

Minimal Informationally Complete Measurements for Pure States

  • Steven T. FlammiaEmail author
  • Andrew Silberfarb
  • Carlton M. Caves


We consider measurements, described by a positive-operator-valued measure (POVM), whose outcome probabilities determine an arbitrary pure state of a D-dimensional quantum system. We call such a measurement a pure-state informationally complete (PS I-complete) POVM. We show that a measurement with 2D−1 outcomes cannot be PS I-complete, and then we construct a POVM with 2D outcomes that suffices, thus showing that a minimal PS I-complete POVM has 2D outcomes. We also consider PS I-complete POVMs that have only rank-one POVM elements and construct an example with 3D−2 outcomes, which is a generalization of the tetrahedral measurement for a qubit. The question of the minimal number of elements in a rank-one PS I-complete POVM is left open.


Quantum state tomography informationally complete measurement Positive Operator-Valued Measure 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Steven T. Flammia
    • 1
    Email author
  • Andrew Silberfarb
    • 1
  • Carlton M. Caves
    • 1
  1. 1.Department of Physics and AstronomyUniversity of New MexicoNew MexicoUSA

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