Symmetric informationally complete quantum measurements

  title={Symmetric informationally complete quantum measurements},
  author={Joseph M. Renes and Robin Blume-Kohout and A. J. Scott and Carlton M. Caves},
  journal={Journal of Mathematical Physics},
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 Cd. 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… 

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