14 research outputs found
Parsing a sequence of qubits
We develop a theoretical framework for frame synchronization, also known as
block synchronization, in the quantum domain which makes it possible to attach
classical and quantum metadata to quantum information over a noisy channel even
when the information source and sink are frame-wise asynchronous. This
eliminates the need of frame synchronization at the hardware level and allows
for parsing qubit sequences during quantum information processing. Our
framework exploits binary constant-weight codes that are self-synchronizing.
Possible applications may include asynchronous quantum communication such as a
self-synchronizing quantum network where one can hop into the channel at any
time, catch the next coming quantum information with a label indicating the
sender, and reply by routing her quantum information with control qubits for
quantum switches all without assuming prior frame synchronization between
users.Comment: 11 pages, 2 figures, 1 table. Final accepted version for publication
in the IEEE Transactions on Information Theor
Perfect difference systems of sets and Jacobi sums
AbstractA perfect (v,{kiā£1ā¤iā¤s},Ļ) difference system of sets (DSS) is a collection of s disjoint ki-subsets Di, 1ā¤iā¤s, of any finite abelian group G of order v such that every non-identity element of G appears exactly Ļ times in the multiset {aābā£aāDi,bāDj,1ā¤iā jā¤s}. In this paper, we give a necessary and sufficient condition in terms of Jacobi sums for a collection {Diā£1ā¤iā¤s} defined in a finite field Fq of order q=ef+1 to be a perfect (q,{kiā£1ā¤iā¤s},Ļ)-DSS, where each Di is a union of cyclotomic cosets of index e (and the zero 0āFq). Also, we give numerical results for the cases e=2,3, and 4
Near-complete external difference families
We introduce and explore near-complete external difference families, a partitioning of the nonidentity elements of a group so that each nonidentity element is expressible as a difference of elements from distinct subsets a fixed number of times. We show that the existence of such an object implies the existence of a near-resolvable design. We provide examples and general constructions of these objects, some of which lead to new parameter families of near-resolvable designs on a non-prime-power number of points. Our constructions employ cyclotomy, partial difference sets, and Galois rings.PostprintPeer reviewe
A Novel Algorithm for Nested Summation and Hypergeometric Expansions
We consider a class of sums over products of Z-sums whose arguments differ by
a symbolic integer. Such sums appear, for instance, in the expansion of Gauss
hypergeometric functions around integer indices that depend on a symbolic
parameter. We present a telescopic algorithm for efficiently converting these
sums into generalized polylogarithms, Z-sums, and cyclotomic harmonic sums for
generic values of this parameter. This algorithm is illustrated by computing
the double pentaladder integrals through ten loops, and a family of massive
self-energy diagrams through in dimensional regularization. We
also outline the general telescopic strategy of this algorithm, which we
anticipate can be applied to other classes of sums.Comment: 36 pages, 2 figures; v2: references added, typos corrected, improved
introduction and comparison with existing methods, matches published versio
1990-1992 Wright State University Graduate Course Catalog
This is a Wright State University graduate course catalog from 1990-1992.https://corescholar.libraries.wright.edu/archives_catalogs/1035/thumbnail.jp
Undergraduate and Graduate Course Descriptions, 2007 Fall
Wright State University undergraduate and graduate course descriptions from Fall 2007