On the connection between mutually unbiased bases and orthogonal Latin squares

We offer a piece of evidence that the problems of finding the number of mutually unbiased bases (MUB) and mutually orthogonal Latin squares (MOLS) might not be equivalent. We study a particular procedure which has been shown to relate the two problems and generates complete sets of MUBs in power-of-prime dimensions and three MUBs in dimension six. For these cases, every square from an augmented set of MOLS has a corresponding MUB. We show that this no longer holds for certain composite dimensions.Comment: 6 pages, submitted to Proceedings of CEWQO 200

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 H\_q, 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^2 and rank r. The q vectors of a basis of H\_q correspond to the q points of a (so-called) neighbour class and the q+1 MUBs answer to the total number of (pairwise disjoint) neighbour classes on the conic.Comment: 4 pages, 1 figure; extended list of references, figure made more illustrative and in colour; v3 - one more figure and section added, paper made easier to follow, references update

State tomography for two qubits using reduced densities

The optimal state determination (or tomography) is studied for a composite system of two qubits when measurements can be performed on one of the qubits and interactions of the two qubits can be implemented. The goal is to minimize the number of interactions to be used. The algebraic method applied in the paper leads to an extension of the concept of mutually unbiased measurements.Comment: 8 pages LATE

The structure of blocks with a Klein four defect group

We prove Erdmann’s conjecture [16] stating that every block with a Klein four defect group has a simple module with trivial source, and deduce from this that Puig’s finiteness conjecture holds for source algebras of blocks with a Klein four defect group. The proof uses the classification of finite simple groups

The Primitive p-Frobenius Groups

Let p be a fixed prime. A finite primitive permutation group G with every twopoint stabilizer G ff;fi being a p-group is called a primitive p-Frobenius group. Using our earlier results on p-intersection subgroups, we give a complete classification of the primitive p-Frobenius groups. 1 Introduction Let \Sigma\Omega denote the symmetric group on a finite set\Omega and G \Sigma\Omega a transitive permutation group. Suppose that every two-point stabilizer G ff;fi is trivial; then a classical result of Frobenius states that G is a semidirect product K : G ff where the normal subgroup K consists precisely of the identity together with all elements g 2 G that do not fix any point of \Omega\Gamma Moreover the point stabilizer G ff acts on K (via conjugation) in such a way that no nontrivial element g 2 G ff has a nontrivial fixed point in K. A permutation group with these properties is called a Frobenius group with Frobenius kernel K. As a consequence of a celebrated theorem of J..

Finite p'-Semiregular Groups

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