Tight informationally complete quantum measurements
Abstract
We introduce a class of informationally complete positiveoperatorvalued measures which are, in analogy with a tight frame, 'as close as possible' to orthonormal bases for the space of quantum states. These measures are distinguished by an exceptionally simple statereconstruction formula which allows 'painless' quantum state tomography. Complete sets of mutually unbiased bases and symmetric informationally complete positiveoperatorvalued measures are both members of this class, the latter being the unique minimal rankone members. Recast as ensembles of pure quantum states, the rankone members are in fact equivalent to weighted 2designs in complex projective space. These measures are shown to be optimal for quantum cloning and linear quantum state tomography.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 October 2006
 DOI:
 10.1088/03054470/39/43/009
 arXiv:
 arXiv:quantph/0604049
 Bibcode:
 2006JPhA...3913507S
 Keywords:

 Quantum Physics
 EPrint:
 20 pages. Final version