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 $\mu$-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 $\mu$-compact sets. Several examples are considered. The main result of the paper is a generalization to $\mu$-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 $\mu$-compact convex sets defined by the slight relaxing of the $\mu$-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

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

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

Three-loop contribution of the Faddeev-Popov ghosts to the β\beta-function of N=1{\cal N}=1 supersymmetric gauge theories and the NSVZ relation

We find the three-loop contribution to the $\beta$-function of ${\cal N}=1$ supersymmetric gauge theories regularized by higher covariant derivatives produced by the supergraphs containing loops of the Faddeev--Popov ghosts. This is done using a recently proposed algorithm, which essentially simplifies such multiloop calculations. The result is presented in the form of an integral of double total derivatives in the momentum space. The considered contribution to the $\beta$-function is compared with the two-loop anomalous dimension of the Faddeev--Popov ghosts. This allows verifying the validity of the NSVZ equation written as a relation between the $\beta$-function and the anomalous dimensions of the quantum superfields. It is demonstrated that in the considered approximation the NSVZ equation is satisfied for the renormalization group functions defined in terms of the bare couplings. The necessity of the nonlinear renormalization for the quantum gauge superfield is also confirmed.Comment: 20 pages, 4 figures, minor corrections, the final version to appear in Eur.Phys.J.

Dynamics of global and segmental strain as a marker of right ventricular contractility recovery in patients after COVID-19 pneumonia

Aim. To study the changes of morphological and functional right ventricular (RV) parameters depending on the severity of coronavirus infection 2019 (COVID-19) pneumonia over long-term follow-up.Material and methods. A total of 200 patients (men, 51,5%, mean age, 51,4±10,9 years) were examined at 2 control visits (3, 12 months after receiving two negative polymerase chain reaction tests). Patients were divided into following groups: group I (n=94) — lung tissue involvement ≥50% according to inhospital chest computed tomography (chest CT), group II (n=106) — lung tissue involvement˂50% according to chest CT.Results. The groups were comparable in key clinical and functional parameters 3 months after COVID-19 pneumonia. Speckle tracking echocardiography (STE) revealed a significant increase in following global longitudinal strain (LS) parameters: RV free wall endocardial LS (-22,7±3,2% and -24,3±3,8% in group I, p<0,001; -23,2±3,5% and -24,5±3,4% in group II, p><0,001), and RV endocardial LS (-21,0±3,1% and -22,5±3,7% in group I, p><0,001, -21,5±3,2% and -22,6±3,3% in group II, p=0,001 ). Significant increase of segmental endocardial LS was revealed in group I in the basal segments of RV free wall (-26,2±5,1% and -28,1±5,1%, p=0,004) and interventricular septum (IVS) (-16,2 [13,9; 19,5]% and -17,5 [14,6; 21,4]%, p=0,024), IVS middle segment (-20,3±4,1% and -21,5±4,8%, p=0,030), as well as in group II in the apical segments of RV free wall (-21,9±6,7% and -24,4±5,2%, p=0,001) and IVS (-23,7±4,7% and -24,9±4,8%, p=0,014). Conclusion. Recovery of RV function during a 12-month follow-up period in patients with both severe and moderate/mild lung involvement in COVID-19 was detected using the STE method.>˂0,001; -23,2±3,5% and -24,5±3,4% in group II, p˂0,001), and RV endocardial LS (-21,0±3,1% and -22,5±3,7% in group I, p˂0,001, -21,5±3,2% and -22,6±3,3% in group II, p=0,001 ). Significant increase of segmental endocardial LS was revealed in group I in the basal segments of RV free wall (-26,2±5,1% and -28,1±5,1%, p=0,004) and interventricular septum (IVS) (-16,2 [13,9; 19,5]% and -17,5 [14,6; 21,4]%, p=0,024), IVS middle segment (-20,3±4,1% and -21,5±4,8%, p=0,030), as well as in group II in the apical segments of RV free wall (-21,9±6,7% and -24,4±5,2%, p=0,001) and IVS (-23,7±4,7% and -24,9±4,8%, p=0,014).Conclusion. Recovery of RV function during a 12-month follow-up period in patients with both severe and moderate/mild lung involvement in COVID-19 was detected using the STE method

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

Three-particle States in Nonrelativistic Four-fermion Model

On a nonrelativistic contact four-fermion model we have shown that the simple Lambda-cut-off prescription together with definite fine-tuning of the Lambda dependency of "bare"quantities lead to self-adjoint semi-bounded Hamiltonian in one-, two- and three-particle sectors. The fixed self-adjoint extension and exact solutions in two-particle sector completely define three-particle problem. The renormalized Faddeev equations for the bound states with Fredholm properties are obtained and analyzed.Comment: 9 pages, LaTex, no figure

Interactions of a j=1j=1 boson in the 2(2j+1)2(2j+1) 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 $2(2j+1)$ component formalism for describing a particle of spin $j$, 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, $p_0^2 -{\bf p}^2=M^2$, 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 $T$ 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