Finite Bruck loops

Bruck loops are Bol loops satisfying the automorphic inverse property. We prove a structure theorem for finite Bruck loops X, showing that X is essentially the direct product of a Bruck loop of odd order with a 2-element Bruck loop. The former class of loops is well understood. We identify the minimal obstructions to the conjecture that all finite 2-element Bruck loops are 2-loops, leaving open the question of whether such obstructions actually exist

A microscopic model for Josephson currents

A microscopic model of a Josephson junction between two superconducting plates is proposed and analysed. For this model, the nonequilibrium steady state of the total system is explicitly constructed and its properties are analysed. In particular, the Josephson current is rigorously computed as a function of the phase difference of the two plates and the typical properties of the Josephson current are recovered

An efficient quantum algorithm for the hidden subgroup problem in extraspecial groups

Extraspecial groups form a remarkable subclass of p-groups. They are also present in quantum information theory, in particular in quantum error correction. We give here a polynomial time quantum algorithm for finding hidden subgroups in extraspecial groups. Our approach is quite different from the recent algorithms presented in [17] and [2] for the Heisenberg group, the extraspecial p-group of size p3 and exponent p. Exploiting certain nice automorphisms of the extraspecial groups we define specific group actions which are used to reduce the problem to hidden subgroup instances in abelian groups that can be dealt with directly.Comment: 10 page

On right conjugacy closed loops of twice prime order

The right conjugacy closed loops of order 2p, where p is an odd prime, are classified up to isomorphism.Comment: Clarified definitions, added some remarks and a tabl

Exact solution of Markovian master equations for quadratic fermi systems: thermal baths, open XY spin chains, and non-equilibrium phase transition

We generalize the method of third quantization to a unified exact treatment of Redfield and Lindblad master equations for open quadratic systems of n fermions in terms of diagonalization of 4n x 4n matrix. Non-equilibrium thermal driving in terms of the Redfield equation is analyzed in detail. We explain how to compute all physically relevant quantities, such as non-equilibrium expectation values of local observables, various entropies or information measures, or time evolution and properties of relaxation. We also discuss how to exactly treat explicitly time dependent problems. The general formalism is then applied to study a thermally driven open XY spin 1/2 chain. We find that recently proposed non-equilibrium quantum phase transition in the open XY chain survives the thermal driving within the Redfield model. In particular, the phase of long-range magnetic correlations can be characterized by hypersensitivity of the non-equilibrium-steady state to external (bath or bulk) parameters. Studying the heat transport we find negative thermal conductance for sufficiently strong thermal driving, as well as non-monotonic dependence of the heat current on the strength of the bath coupling.Comment: 24 pages, 12 figures, submitted to New Journal of Physics, Focus issue "Quantum Information and Many-Body Theory

Policy for Robust Space-based Earth Science, Technology and Applications

Satellite remote sensing technology has contributed to the transformation of multiple earth science domains, putting space observations at the forefront of innovation in earth science. With new satellite missions being launched every year, new types of earth science data are being incorporated into science models and decision-making systems in a broad array of organizations. Policy guidance can influence the degree to which user needs influence mission design and when, and ensure that satellite missions serve both the scientific and user communities without becoming unfocused and overly expensive. By considering the needs of the user community early on in the mission-design process, agencies can ensure that satellites meet the needs of multiple constituencies. This paper describes the mission development process in NASA and ESA and compares and contrasts the successes and challenges faced by these agencies as they try to balance science and applications within their missions

Braided racks, Hurwitz actions and Nichols algebras with many cubic relations

We classify Nichols algebras of irreducible Yetter-Drinfeld modules over groups such that the underlying rack is braided and the homogeneous component of degree three of the Nichols algebra satisfies a given inequality. This assumption turns out to be equivalent to a factorization assumption on the Hilbert series. Besides the known Nichols algebras we obtain a new example. Our method is based on a combinatorial invariant of the Hurwitz orbits with respect to the action of the braid group on three strands.Comment: v2: 35 pages, 6 tables, 14 figure

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

Conversion of a general quantum stabilizer code to an entanglement distillation protocol

We show how to convert a quantum stabilizer code to a one-way or two-way entanglement distillation protocol. The proposed conversion method is a generalization of those of Shor-Preskill and Nielsen-Chuang. The recurrence protocol and the quantum privacy amplification protocol are equivalent to the protocols converted from [[2,1]] stabilizer codes. We also give an example of a two-way protocol converted from a stabilizer better than the recurrence protocol and the quantum privacy amplification protocol. The distillable entanglement by the class of one-way protocols converted from stabilizer codes for a certain class of states is equal to or greater than the achievable rate of stabilizer codes over the channel corresponding to the distilled state, and they can distill asymptotically more entanglement from a very noisy Werner state than the hashing protocol.Comment: LaTeX2e, 18 pages, 1 figure. Version 4 added an example of two-way protocols better than the recurrence protocol and the quantum privacy amplification protocol. Version 2 added the quantum privacy amplification protocol as an example converted from a stabilizer code, and corrected many errors. Results unchanged from V