Symmetric Informationally Complete Quantum Measurements
<|reference_start|>Symmetric Informationally Complete Quantum Measurements: 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.<|reference_end|>
@article{renes2003symmetric,
    title={Symmetric Informationally Complete Quantum Measurements},
    author={Joseph M. Renes, Robin Blume-Kohout, A. J. Scott, and Carlton M. Caves},
    journal={J. Math. Phys. 45, 2171 (2004)},
    year={2003},
    doi={10.1063/1.1737053},
    archivePrefix={arXiv},
    eprint={quant-ph/0310075},
    primaryClass={quant-ph cs.IT math.FA math.IT}
}