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It is shown that the Veldkamp space of the unique generalized quadrangle GQ(2,4) is isomor-phic to PG(5,2). Since the GQ(2,4) features only two kinds of geometric hyperplanes, namely point's perp-sets and GQ(2,2)s, the 63 points of PG(5,2) split into two families; 27 being represented by perp-sets and 36 by GQ(2,2)s. The 651 lines of PG(5,2) are found to(More)
The set of 63 real generalized Pauli matrices of three-qubits can be factored into two subsets of 35 symmetric and 28 antisymmetric elements. This splitting is shown to be completely embodied in the properties of the Fano plane; the elements of the former set being in a bijective correspondence with the 7 points, 7 lines and 21 flags, whereas those of the(More)
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(More)
We study the problem of converting a product of Greenberger-Horne-Zeilinger (GHZ) states shared by subsets of several parties in an arbitrary way into GHZ states shared by every party. Our result is that if SLOCC transformations are allowed, then the best asymptotic rate is the minimum of bipartite log-ranks of the initial state. This generalizes a result(More)
We present an upper bound on the exponent of the asymptotic behaviour of the tensor rank of a family of tensors defined by the complete graph on k vertices. For k ≥ 4, we show that the exponent per edge is at most 0.77, outperforming the best known upper bound on the exponent per edge for matrix multiplication (k = 3), which is approximately 0.79. We raise(More)
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