654 research outputs found
Families of twisted tensor product codes
Using geometric properties of the variety \cV_{r,t}, the image under the
Grassmannian map of a Desarguesian -spread of \PG(rt-1,q), we
introduce error correcting codes related to the twisted tensor product
construction, producing several families of constacyclic codes. We exactly
determine the parameters of these codes and characterise the words of minimum
weight.Comment: Keywords: Segre Product, Veronesean, Grassmannian, Desarguesian
spread, Subgeometry, Twisted Product, Constacyclic error correcting code,
Minimum weigh
Weaving Worldsheet Supermultiplets from the Worldlines Within
Using the fact that every worldsheet is ruled by two (light-cone) copies of
worldlines, the recent classification of off-shell supermultiplets of
N-extended worldline supersymmetry is extended to construct standard off-shell
and also unidextrous (on the half-shell) supermultiplets of worldsheet
(p,q)-supersymmetry with no central extension. In the process, a new class of
error-correcting (even-split doubly-even linear block) codes is introduced and
classified for , providing a graphical method for classification of
such codes and supermultiplets. This also classifies quotients by such codes,
of which many are not tensor products of worldline factors. Also,
supermultiplets that admit a complex structure are found to be depictable by
graphs that have a hallmark twisted reflection symmetry.Comment: Extended version, with added discussion of complex and quaternionic
tensor products demonstrating that certain quotient supermultiplets do not
factorize over any ground fiel
A Non-Commuting Stabilizer Formalism
We propose a non-commutative extension of the Pauli stabilizer formalism. The
aim is to describe a class of many-body quantum states which is richer than the
standard Pauli stabilizer states. In our framework, stabilizer operators are
tensor products of single-qubit operators drawn from the group , where and . We
provide techniques to efficiently compute various properties related to
bipartite entanglement, expectation values of local observables, preparation by
means of quantum circuits, parent Hamiltonians etc. We also highlight
significant differences compared to the Pauli stabilizer formalism. In
particular, we give examples of states in our formalism which cannot arise in
the Pauli stabilizer formalism, such as topological models that support
non-Abelian anyons.Comment: 52 page
Generalized Long-Moody functors
In this paper, we generalize the Long-Moody construction for representations
of braid groups to other groups, such as mapping class groups of surfaces.
Moreover, we introduce Long-Moody endofunctors over a functor category that
encodes representations of a family of groups. In this context, notions of
polynomial functor are defined; these play an important role in the study of
homological stability. We prove that, under some additional assumptions, a
Long-Moody functor increases the (very) strong (respectively weak) polynomial
degree of functors by one
On the Gauge Equivalence of Twisted Quantum Doubles of Elementary Abelian and Extra-Special 2-Groups
We establish braided tensor equivalences among module categories over the
twisted quantum double of a finite group defined by an extension of a group H
by an abelian group, with 3-cocycle inflated from a 3-cocycle on H. We also
prove that the canonical ribbon structure of the module category of any twisted
quantum double of a finite group is preserved by braided tensor equivalences.
We give two main applications: first, if G is an extra-special 2-group of width
at least 2, we show that the quantum double of G twisted by a 3-cocycle w is
gauge equivalent to a twisted quantum double of an elementary abelian 2-group
if, and only if, w^2 is trivial; second, we discuss the gauge equivalence
classes of twisted quantum doubles of groups of order 8, and classify the
braided tensor equivalence classes of these quasi-triangular quasi-bialgebras.
It turns out that there are exactly 20 such equivalence classes.Comment: 27 pages, LateX, a few of typos in v2 correcte
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