### Abstract

We introduce a point-line incidence geometry in which the commutation relations of the real Pauli group of multiple qubits are fully encoded. Its points are pairs of Pauli operators differing in sign, and each line contains three pairwise commuting operators any of which is the product of the other two (up to sign). We study the properties of its Veldkamp space enabling us to identify subsets of operators which are distinguished from the geometric point of view. These are geometric hyperplanes and pairwise intersections. Among the geometric hyperplanes, one can find the set of self-dual operators with respect to the Wootters spin-flip operation well known from studies concerning multiqubit entanglement measures. In the two- and three-qubit cases, a class of hyperplanes gives rise to Mermin squares and other generalized quadrangles. In the three-qubit case, the hyperplane with points corresponding to the 27 Wootters self-dual operators is just the underlying geometry of the E _{6(6)} symmetric entropy formula describing black holes and strings in five dimensions.

Original language | English |
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Article number | 125303 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 43 |

Issue number | 12 |

DOIs | |

Publication status | Published - márc. 19 2010 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

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## Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*43*(12), [125303]. https://doi.org/10.1088/1751-8113/43/12/125303