On PSI-complete and PSIR-complete measurements

Details On PSI-complete and PSIR-complete measurements On PSI-complete and PSIR-complete measurements

2004-07-11

arxiv.org/abs/quant-ph/0407078v2

Phys. Rev. A 70, 052107 (2004).

Physics

Quantum Physics

9 pages, LaTeX, no figures v2: Added comment about MUBs; corrected typos

Scientific paper

10.1103/PhysRevA.70.052107

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.

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