1305.6545 (Gilad Gour)

General symmetric informationally complete measurements exist in all
dimensions    [PDF]

Gilad Gour

We construct the set of all general (i.e. not necessarily rank 1) symmetric informationally complete (SIC) positive operator valued measures (POVMs), and thereby show that SIC-POVMs that are not necessarily rank 1 exist in any finite dimension d. In particular, we show that any orthonormal basis of a real vector space of dimension d^2-1 corresponds to some general SIC POVM and vice versa. Our constructed set of all general SIC-POVMs contains weak SIC-POVMs for which each POVM element can be made arbitrarily close to a multiple times the identity. On the other hand, it remains open if for all finite dimensions our constructed family contains a rank 1 SIC-POVM.

View original: http://arxiv.org/abs/1305.6545