Wednesday, May 29, 2013

1305.6545 (Gilad Gour)

General symmetric informationally complete measurements exist in all

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.
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