Entanglement and quantum combinatorial designs

@article{Goyeneche2017EntanglementAQ,
  title={Entanglement and quantum combinatorial designs},
  author={Dardo Goyeneche and Zahra Raissi and Sara Di Martino and Karol Życzkowski},
  journal={Physical Review A},
  year={2017}
}
We introduce the notion of quantum orthogonal arrays as a generalization of orthogonal arrays. These quantum combinatorial designs naturally induce the concepts of quantum Latin squares, cubes, hypercubes and a notion of orthogonality between them. Furthermore, quantum orthogonal arrays are one-to-one related to $k$-uniform states, i.e., pure states such that every reduction to $k$ parties is maximally mixed. We derive quantum orthogonal arrays having an arbitrary large number of columns and… 

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