Symmetric informationally complete quantum measurements
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We consider the existence in arbitrary finite dimensions d of a positive operator valued measure (POVM) comprised of d2 rank-one operators all of whose operator inner products are equal. Such a set is called a "symmetric, informationally complete" POVM (SIC-POVM) and is equivalent to a set of d2 equiangular lines in d. SIC-POVMs are relevant for quantum state tomography, quantum cryptography, and foundational issues in quantum mechanics. We construct SIC-POVMs in dimensions two, three, and four. We further conjecture that a particular kind of group-covariant SIC-POVM exists in arbitrary dimensions, providing numerical results up to dimension 45 to bolster this claim.鲰04 American Institute of Physics.
Journal of Mathematical Physics
Copyright 2004 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Mathematical Physics, Vol. 45(6), pp. 2171-2180 and may be found at http://dx.doi.org/10.1063/1.1737053.