Compounds of symmetric informationally complete measurements and their application in quantum key distribution

@article{Tavakoli2020CompoundsOS,
  title={Compounds of symmetric informationally complete measurements and their application in quantum key distribution},
  author={Armin Tavakoli and Ingemar Bengtsson and Nicolas Gisin and Joseph M. Renes},
  journal={arXiv: Quantum Physics},
  year={2020}
}
Symmetric informationally complete measurements (SICs) are elegant, celebrated and broadly useful discrete structures in Hilbert space. We introduce a more sophisticated discrete structure compounded by several SICs. A SIC-compound is defined to be a collection of $d^3$ vectors in $d$-dimensional Hilbert space that can be partitioned in two different ways: into $d$ SICs and into $d^2$ orthonormal bases. While a priori their existence may appear unlikely when $d>2$, we surprisingly answer it in… 

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