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Minimal Informationally Complete Measurements for Pure States

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Abstract

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.

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico, 87131–1156, USA

    Steven T. Flammia, Andrew Silberfarb & Carlton M. Caves

Authors
  1. Steven T. Flammia
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  2. Andrew Silberfarb
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  3. Carlton M. Caves
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Correspondence to Steven T. Flammia.

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Flammia, S.T., Silberfarb, A. & Caves, C.M. Minimal Informationally Complete Measurements for Pure States. Found Phys 35, 1985–2006 (2005). https://doi.org/10.1007/s10701-005-8658-z

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