Physics – Quantum Physics
Scientific paper
2010-03-18
J. Phys. A: Math. Theor. 43 305305 (2010)
Physics
Quantum Physics
30 pages, 1 figure, section 4 revised and extended, published in J. Phys. A: Math. Theor. 43, 305305 (2010)
Scientific paper
We show that in prime dimensions not equal to three, each group covariant symmetric informationally complete positive operator valued measure (SIC~POVM) is covariant with respect to a unique Heisenberg--Weyl (HW) group. Moreover, the symmetry group of the SIC~POVM is a subgroup of the Clifford group. Hence, two SIC~POVMs covariant with respect to the HW group are unitarily or antiunitarily equivalent if and only if they are on the same orbit of the extended Clifford group. In dimension three, each group covariant SIC~POVM may be covariant with respect to three or nine HW groups, and the symmetry group of the SIC~POVM is a subgroup of at least one of the Clifford groups of these HW groups respectively. There may exist two or three orbits of equivalent SIC~POVMs for each group covariant SIC~POVM, depending on the order of its symmetry group. We then establish a complete equivalence relation among group covariant SIC~POVMs in dimension three, and classify inequivalent ones according to the geometric phases associated with fiducial vectors. Finally, we uncover additional SIC~POVMs by regrouping of the fiducial vectors from different SIC~POVMs which may or may not be on the same orbit of the extended Clifford group.
No associations
LandOfFree
SIC~POVMs and Clifford groups in prime dimensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with SIC~POVMs and Clifford groups in prime dimensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and SIC~POVMs and Clifford groups in prime dimensions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-700603