29 research outputs found
Reversibility conditions for quantum channels and their applications
A necessary condition for reversibility (sufficiency) of a quantum channel
with respect to complete families of states with bounded rank is obtained. A
full description (up to isometrical equivalence) of all quantum channels
reversible with respect to orthogonal and nonorthogonal complete families of
pure states is given. Some applications in quantum information theory are
considered.
The main results can be formulated in terms of the operator algebras theory
(as conditions for reversibility of channels between algebras of all bounded
operators).Comment: 28 pages, this version contains strengthened results of the previous
one and of arXiv:1106.3297; to appear in Sbornik: Mathematics, 204:7 (2013
Generalized compactness in linear spaces and its applications
The class of subsets of locally convex spaces called -compact sets is
considered. This class contains all compact sets as well as several noncompact
sets widely used in applications. It is shown that many results well known for
compact sets can be generalized to -compact sets. Several examples are
considered.
The main result of the paper is a generalization to -compact convex sets
of the Vesterstrom-O'Brien theorem showing equivalence of the particular
properties of a compact convex set (s.t. openness of the mixture map, openness
of the barycenter map and of its restriction to maximal measures, continuity of
a convex hull of any continuous function, continuity of a convex hull of any
concave continuous function). It is shown that the Vesterstrom-O'Brien theorem
does not hold for pointwise -compact convex sets defined by the slight
relaxing of the -compactness condition. Applications of the obtained
results to quantum information theory are considered.Comment: 27 pages, the minor corrections have been mad
On properties of the space of quantum states and their application to construction of entanglement monotones
We consider two properties of the set of quantum states as a convex
topological space and some their implications concerning the notions of a
convex hull and of a convex roof of a function defined on a subset of quantum
states.
By using these results we analyze two infinite-dimensional versions (discrete
and continuous) of the convex roof construction of entanglement monotones,
which is widely used in finite dimensions. It is shown that the discrete
version may be 'false' in the sense that the resulting functions may not
possess the main property of entanglement monotones while the continuous
version can be considered as a 'true' generalized convex roof construction. We
give several examples of entanglement monotones produced by this construction.
In particular, we consider an infinite-dimensional generalization of the notion
of Entanglement of Formation and study its properties.Comment: 34 pages, the minor corrections have been mad
One-mode Bosonic Gaussian channels: a full weak-degradability classification
A complete degradability analysis of one-mode Gaussian Bosonic channels is
presented. We show that apart from the class of channels which are unitarily
equivalent to the channels with additive classical noise, these maps can be
characterized in terms of weak- and/or anti-degradability. Furthermore a new
set of channels which have null quantum capacity is identified. This is done by
exploiting the composition rules of one-mode Gaussian maps and the fact that
anti-degradable channels can not be used to transfer quantum information.Comment: 23 pages, 3 figure