A Notable Relation between N-Qubit and 2^{N-1}-Qubit Pauli Groups via Binary LGr(N,2N)

@article{Holweck2014ANR,
  title={A Notable Relation between N-Qubit and 2^\{N-1\}-Qubit Pauli Groups via Binary LGr(N,2N)},
  author={F. Holweck and M. Saniga and P. L'evay},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  year={2014},
  volume={10},
  pages={041}
}
Employing the fact that the geometry of the $N$-qubit ($N \geq 2$) Pauli group is embodied in the structure of the symplectic polar space $\mathcal{W}(2N-1,\,2)$ and using properties of the Lagrangian Grassmannian $LGr(N,\,2N)$ defined over the smallest Galois field, it is demonstrated that there exists a bijection between the set of maximum sets of mutually commuting elements of the $N$-qubit Pauli group and a certain subset of elements of the $2^{N-1}$-qubit Pauli group. In order to reveal… Expand

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