ar X iv : m at h - ph / 0 50 60 57 v 2 2 6 Ju l 2 00 5 Hjelmslev Geometry of Mutually Unbiased Bases

ar X iv : m at h - ph / 0 50 60 57 v 3 8 N ov 2 00 5 Hjelmslev Geometry of Mutually Unbiased Bases

The basic combinatorial properties of a complete set of mutually unbiased bases (MUBs) of a q-dimensional Hilbert space Hq, q = p with p being a prime and r a positive integer, are shown to be qualitatively mimicked by the configuration of points lying on a proper conic in a projective Hjelmslev plane defined over a Galois ring of characteristic p and rank r. The q vectors of a basis of Hq corr...

ar X iv : m at h - ph / 0 50 60 57 v 1 2 2 Ju n 20 05 Hjelmslev Geometry of Mutually Unbiased Bases

The basic combinatorial properties of a complete set of mutually unbiased bases (MUBs) of a q-dimensional Hilbert space Hq, q = p r with p being a prime and r a positive integer, are shown to be qualitatively mimicked by the configuration of points lying on a proper conic in a projective Hjelmslev plane defined over a Galois ring of characteristic p and rank r. The q vectors of a basis of Hq co...

ar X iv : m at h - ph / 0 60 70 40 v 1 2 0 Ju l 2 00 6 Invariant Form of BK - factorization and its Applications

ar X iv : 0 80 6 . 07 26 v 1 [ qu an t - ph ] 4 J un 2 00 8 Mutually unbiased bases in discrete phase space

We work out the phase-space structure for a system of n qubits. We replace the field of real numbers that label the axes of the continuous phase space by the finite field GF(2n) and investigate the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We provide...

ar X iv : m at h - ph / 0 50 10 64 v 6 2 5 Ju l 2 00 6 Hidden Consequence of Active Local Lorentz Invariance ∗

In this paper we investigate a hidden consequence of the hypothesis that Lagrangians and field equations must be invariant under active local Lorentz transformations. We show that this hypothesis implies in an equivalence between spacetime structures with several curvature and torsion possibilities.