4,265 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
New -designs from strong difference families
Strong difference families are an interesting class of discrete structures
which can be used to derive relative difference families. Relative difference
families are closely related to -designs, and have applications in
constructions for many significant codes, such as optical orthogonal codes and
optical orthogonal signature pattern codes. In this paper, with a careful use
of cyclotomic conditions attached to strong difference families, we improve the
lower bound on the asymptotic existence results of -DFs for .
We improve Buratti's existence results for - designs and
- designs, and establish the existence of seven new
- designs for
,
.Comment: Version 1 is named "Improved cyclotomic conditions leading to new
2-designs: the use of strong difference families". Major revision according
to the referees' comment
Frame difference families and resolvable balanced incomplete block designs
Frame difference families, which can be obtained via a careful use of
cyclotomic conditions attached to strong difference families, play an important
role in direct constructions for resolvable balanced incomplete block designs.
We establish asymptotic existences for several classes of frame difference
families. As corollaries new infinite families of 1-rotational
-RBIBDs over are
derived, and the existence of -RBIBDs is discussed. We construct
-RBIBDs for , whose
existence were previously in doubt. As applications, we establish asymptotic
existences for an infinite family of optimal constant composition codes and an
infinite family of strictly optimal frequency hopping sequences.Comment: arXiv admin note: text overlap with arXiv:1702.0750
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