Symmetric informationally complete quantum measurements
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- 1 June 2004
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 45 (6), 2171-2180
- https://doi.org/10.1063/1.1737053
Abstract
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.Full TexKeywords
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