31,805 research outputs found
Construction of self-dual normal bases and their complexity
Recent work of Pickett has given a construction of self-dual normal bases for
extensions of finite fields, whenever they exist. In this article we present
these results in an explicit and constructive manner and apply them, through
computer search, to identify the lowest complexity of self-dual normal bases
for extensions of low degree. Comparisons to similar searches amongst normal
bases show that the lowest complexity is often achieved from a self-dual normal
basis
Group Representations, Error Bases and Quantum Codes
This report continues the discussion of unitary error bases and quantum codes
begun in "Non-binary Unitary Error Bases and Quantum Codes". Nice error bases
are characterized in terms of the existence of certain characters in a group. A
general construction for error bases which are non-abelian over the center is
given. The method for obtaining codes due to Calderbank et al. is generalized
and expressed purely in representation theoretic terms. The significance of the
inertia subgroup both for constructing codes and obtaining the set of
transversally implementable operations is demonstrated.Comment: 11 pages, preliminary repor
Finding decompositions of a class of separable states
By definition a separable state has the form \sum A_i \otimes B_i, where 0
\leq A_i, B_i for each i. In this paper we consider the class of states which
admit such a decomposition with B_1, ..., B_p having independent images. We
give a simple intrinsic characterization of this class of states, and starting
with a density matrix in this class, describe a procedure to find such a
decomposition with B_1, ..., B_p having independent images, and A_1, ..., A_p
being distinct with unit trace. Such a decomposition is unique, and we relate
this to the facial structure of the set of separable states.
A special subclass of such separable states are those for which the rank of
the matrix matches one marginal rank. Such states have arisen in previous
studies of separability (e.g., they are known to be a class for which the PPT
condition is equivalent to separability).
The states investigated also include a class that corresponds (under the
Choi-Jamio{\l}kowski isomorphism) to the quantum channels called
quantum-classical and classical-quantum by Holevo
Third quantization
The basic ideas of second quantization and Fock space are extended to density
operator states, used in treatments of open many-body systems. This can be done
for fermions and bosons. While the former only requires the use of a
non-orthogonal basis, the latter requires the introduction of a dual set of
spaces. In both cases an operator algebra closely resembling the canonical one
is developed and used to define the dual sets of bases. We here concentrated on
the bosonic case where the unboundedness of the operators requires the
definitions of dual spaces to support the pair of bases. Some applications,
mainly to non-equilibrium steady states, will be mentioned.Comment: To appear in the Proceedings of Symposium Symmetries in Nature in
memoriam Marcos Moshinsky.
http://www.cicc.unam.mx/activities/2010/SymmetriesInNature/index.htm
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