Symmetric Informationally Complete Quantum Measurements

Details Symmetric Informationally Complete Quantum Measurements Symmetric Informationally Complete Quantum Measurements

2003-10-13

arxiv.org/abs/quant-ph/0310075v1

J. Math. Phys. 45, 2171 (2004)

Physics

Quantum Physics

8 pages

Scientific paper

10.1063/1.1737053

We consider the existence in arbitrary finite dimensions d of a POVM comprised of d^2 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 d^2 equiangular lines in C^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.

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