Symmetric Informationally Complete Measurements of Arbitrary Rank

Details Symmetric Informationally Complete Measurements of Arbitrary Rank Symmetric Informationally Complete Measurements of Arbitrary Rank

2006-11-27

arxiv.org/abs/quant-ph/0611260v1

Physics

Quantum Physics

Contribution to proceedings of International Conference on Quantum Optics, Minsk, 2006

Scientific paper

10.1134/S0030400X07090111

There has been much interest in so-called SIC-POVMs: rank 1 symmetric informationally complete positive operator valued measures. In this paper we discuss the larger class of POVMs which are symmetric and informationally complete but not necessarily rank 1. This class of POVMs is of some independent interest. In particular it includes a POVM which is closely related to the discrete Wigner function. However, it is interesting mainly because of the light it casts on the problem of constructing rank 1 symmetric informationally complete POVMs. In this connection we derive an extremal condition alternative to the one derived by Renes et al.

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