On PSI-complete and PSIR-complete measurements
Quantum Physics
2009-11-10 v2
Abstract
I construct a POVM which has 2d rank-one elements and which is informationally complete for generic pure states in d dimensions, thus confirming a conjecture made by Flammia, Silberfarb, and Caves (quant-ph/0404137). I show that if a rank-one POVM is required to be informationally complete for all pure states in d dimensions, it must have at least 3d-2 elements. I also show that, in a POVM which is informationally complete for all pure states in d dimensions, for any vector there must be at least 2d-1 POVM elements which do not annihilate that vector.
Cite
@article{arxiv.quant-ph/0407078,
title = {On PSI-complete and PSIR-complete measurements},
author = {J. Finkelstein},
journal= {arXiv preprint arXiv:quant-ph/0407078},
year = {2009}
}
Comments
9 pages, LaTeX, no figures v2: Added comment about MUBs; corrected typos