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Papers in Algebra

Algebra papers in Mathematics, Q

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Papers 1 - 20 of 21 in Algebra, Q
  1. Quantum cryptography could well be the first application of quantum mechanics at the single-quantum level. The rapid progress in both theory and experiment in recent years is reviewed, with emphasis on open questions and technological issues.
  2. The purpose of this Note is to unify quantum groups and star-products under a general umbrella: quantum groupoids. It is shown that a quantum groupoid naturally gives rise to a Lie bialgebroid as a classical limit. The converse question, i.e., the…
  3. We classify the compact quantum groups acting on 4 points. These are the quantum subgroups of the quantum permutation group $\mathcal Q_4$. Our main tool is a new presentation for the algebra $\rm C(\mathcal Q_4)$, corresponding to an isomorphism of…
  4. This paper investigates quantum logic from the perspective of categorical logic, and starts from minimal assumptions, namely the existence of involutions/daggers and kernels. The resulting structures turn out to (1) encompass many examples of…
  5. In this paper a programming language, qGCL,is presented for the expression of quantum algorithms. It contains the features re- quired to program a ‘universal’ quantum computer (including initiali- sation and observation), has a formal semantics and…
  6. We study the discrete-time quantum walk-based search for a marked vertex on a graph. By considering various structures in which not all vertices are equivalent, we investigate the relationship between the successful search probability and the…
  7. We introduce a large equivalence class of graph properties, all of which are shared by so-called random graphs. Unlike random graphs, however, it is often relatively easy to verify that a particular family of graphs possesses some property in this…
  8. We present a practical and efficient means to compute the singular value decomposition (SVD) of a real or complex quaternion matrix A based on bidiagonalization of A to a real or complex bidiagonal matrix B using quaternionic Householder…
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