462 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
IBM: parameter symmetry, hidden symmetries and transformations of boson operators
A symmetry of the parameter space of interacting boson models IBM-1 and IBM-2
is studied. The symmetry is associated with linear canonical transformations of
boson operators, or, equivalently, with the existence of different realizations
of the symmetry algebras of the models. The relevance of the parameter symmetry
to physical observables is discussed.Comment: LATEX, 11 pages including 1 eps figure and 1 table prepared as an eps
figure; a talk given by A. M. Siirokov at XXII Symposium on Nuclear Physics,
Oaxtepec, Morelos, M\'exico, 5--8 January, 1999; to be published in Revista
Mex. Fi
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
Fine-Tuning Renormalization and Two-particle States in Nonrelativistic Four-fermion Model
Various exact solutions of two-particle eigenvalue problems for
nonrelativistic contact four-fermion current-current interaction are obtained.
Specifics of Goldstone mode is investigated. The connection between a
renormalization procedure and construction of self-adjoint extensions is
revealed.Comment: 13 pages, LaTex, no figures, to be published in IJMP
Multi-channel phase-equivalent transformation and supersymmetry
Phase-equivalent transformation of local interaction is generalized to the
multi-channel case. Generally, the transformation does not change the number of
the bound states in the system and their energies. However, with a special
choice of the parameters, the transformation removes one of the bound states
and is equivalent to the multi-channel supersymmetry transformation recently
suggested by Sparenberg and Baye. Using the transformation, it is also possible
to add a bound state to the discrete spectrum of the system at a given energy
if the angular momentum at least in one of the coupled channels .Comment: 9 pages, revtex; to be published in Phys. At. Nucl. (Oct. 2000
CONSTRUCTIVE DESCRIPTION OF FUNCTION CLASSES ON SURFACES IN R^3 AND R^4
Functional classes on a curve in a plane (a partial case
of a spatial curve) can be described by the approximation speed by functions that are harmonic in three-dimensional neighbourhoods of the curve. No constructive description of functional classes on rather general surfaces in R 3 and R 4 has been presented in literature so far. The main result of the paper is Theorem 1
Relativistic Operator Description of Photon Polarization
We present an operator approach to the description of photon polarization,
based on Wigner's concept of elementary relativistic systems. The theory of
unitary representations of the Poincare group, and of parity, are exploited to
construct spinlike operators acting on the polarization states of a photon at
each fixed energy momentum. The nontrivial topological features of these
representations relevant for massless particles, and the departures from the
treatment of massive finite spin representations, are highlighted and
addressed.Comment: Revtex 9 page
A Discrete Version of the Inverse Scattering Problem and the J-matrix Method
The problem of the Hamiltonian matrix in the oscillator and Laguerre basis
construction from the S-matrix is treated in the context of the algebraic
analogue of the Marchenko method.Comment: 11 pages. The Laguerre basis case is adde
Interactions of a boson in the component theory
The amplitudes for boson-boson and fermion-boson interactions are calculated
in the second order of perturbation theory in the Lobachevsky space. An
essential ingredient of the used model is the Weinberg's component
formalism for describing a particle of spin , recently developed
substantially. The boson-boson amplitude is then compared with the two-fermion
amplitude obtained long ago by Skachkov on the ground of the hamiltonian
formulation of quantum field theory on the mass hyperboloid, , proposed by Kadyshevsky. The parametrization of the amplitudes by
means of the momentum transfer in the Lobachevsky space leads to same spin
structures in the expressions of matrices for the fermion and the boson
cases. However, certain differences are found. Possible physical applications
are discussed.Comment: REVTeX 3.0 file. 12pp. Substantially revised version of IFUNAM
preprints FT-93-24, FT-93-3
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