4,971 research outputs found
Role of Partial Transpose and Generalized Choi maps in Quantum Dynamical Semigroups involving Separable and Entangled States
Power symmetric matrices defned and studied by R. Sinkhorn (1981) and their
generalization by R.B. Bapat, S.K. Jain and K. Manjunatha Prasad (1999) have
been utilized to give positive block matrices with trace one possessing
positive partial transpose, the so-called PPT states. Another method to
construct such PPT states is given, it uses the form of a matrix unitarily
equivalent to its transpose obtained by S.R. Garcia and J.E. Tener (2012).
Evolvement or suppression of separability or entanglement of various levels for
a quantum dynamical semigroup of completely positive maps has been studied
using Choi-Jamiolkowsky matrix of such maps and the famous Horodecki's criteria
(1996). A Trichotomy Theorem has been proved, and examples have been given that
depend mainly on generalized Choi maps and clearly distinguish the levels of
entanglement breaking.Comment: A few corrections and changes in view of discussion with Matthias
Christand
Hypergroup Deformations of Semigroups
We view the well-known example of the dual of a countable compact hypergroup,
motivated by the orbit space of p-adic integers by Dunkl and Ramirez (1975), as
hypergroup deformation of the max semigroup structure on the linearly ordered
set of the non-negative integers along the diagonal. This works
as motivation for us to study hypergroups or semi convolution spaces arising
from "max" semigroups or general commutative semigroups via hypergroup
deformation on idempotents.Comment: 28 pages, 1 Table, This version is a truncated version with fourth
section deleted from version 3, which is being developed into a separate
paper. The title and abstract have been changed accordingl
Involutions and Trivolutions in Algebras Related to Second Duals of Group Algebras
We define a trivolution on a complex algebra as a non-zero
conjugate-linear, anti-homomorphism on , which is a generalized
inverse of itself, that is, . We give several characterizations of
trivolutions and show with examples that they appear naturally on many Banach
algebras, particularly those arising from group algebras. We give several
results on the existence or non-existence of involutions on the dual of a
topologically introverted space. We investigate conditions under which the dual
of a topologically introverted space admits trivolutions
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