On perturbations of the isometric semigroup of shifts on the semiaxis

We study perturbations $(\tilde\tau_t)_{t\ge 0}$ of the semigroup of shifts $(\tau_t)_{t\ge 0}$ on $L^2(\R_+)$ with the property that $\tilde\tau_t - \tau_t$ belongs to a certain Schatten-von Neumann class \gS_p with $p\ge 1$. We show that, for the unitary component in the Wold-Kolmogorov decomposition of the cogenerator of the semigroup $(\tilde\tau_t)_{t\ge 0}$, {\it any singular} spectral type may be achieved by \gS_1 perturbations. We provide an explicit construction for a perturbation with a given spectral type based on the theory of model spaces of the Hardy space $H^2$. Also we show that we may obtain {\it any} prescribed spectral type for the unitary component of the perturbed semigroup by a perturbation from the class \gS_p with $p>1$

Non-additivity of Renyi entropy and Dvoretzky's Theorem

The goal of this note is to show that the analysis of the minimum output p-Renyi entropy of a typical quantum channel essentially amounts to applying Milman's version of Dvoretzky's Theorem about almost Euclidean sections of high-dimensional convex bodies. This conceptually simplifies the (nonconstructive) argument by Hayden-Winter disproving the additivity conjecture for the minimal output p-Renyi entropy (for p>1).Comment: 8 pages, LaTeX; v2: added and updated references, minor editorial changes, no content change

Evolution equation of quantum tomograms for a driven oscillator in the case of the general linear quantization

The symlectic quantum tomography for the general linear quantization is introduced. Using the approach based upon the Wigner function techniques the evolution equation of quantum tomograms is derived for a parametric driven oscillator.Comment: 11 page

Methodology for failure analysis of complex technical systems and prevention of their consequences

The paper presents a study on the methodology of failures and their possible consequences analysis. Analysis of failures and their consequences is carried out for newly developed or modernized products and it is one of main activities in the reliability assurance system. The methodology is applied to the analysis of all designed systems, starting from the earliest stage of development, in order to evaluate the approach to development and compare the advantages of the design solution. The considered analysis of failures and their consequences of components is a part of the complex analysis of reliability of the whole product. Depending on the complexity of the design and the available data, a particular approach may be chosen for the analysis. In one case, it is a structural approach, in which a list of individual elements and their possible failures is compiled. In another case, it is the functional approach, which is based on the statement that each element must perform a number of functions that can be classified as solutions. The results provide a scheme for conducting the analysis and finding solutions to prevent them. The conclusions say that the level of detail determines the level at which failures are postulated

Отзыв на монографию В.Н. Шолохова, Б.В. Бухаркина, П.И. Лепэдату «Ультразвуковая томография в диагностике рака предстательной железы»

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Minimum output entropy of bosonic channels: a conjecture

The von Neumann entropy at the output of a bosonic channel with thermal noise is analyzed. Coherent-state inputs are conjectured to minimize this output entropy. Physical and mathematical evidence in support of the conjecture is provided. A stronger conjecture--that output states resulting from coherent-state inputs majorize the output states from other inputs--is also discussed.Comment: 15 pages, 12 figure

On calculating the mean values of quantum observables in the optical tomography representation

Given a density operator $\hat \rho$ the optical tomography map defines a one-parameter set of probability distributions $w_{\hat \rho}(X,\phi),\ \phi \in [0,2\pi),$ on the real line allowing to reconstruct $\hat \rho$. We introduce a dual map from the special class $\mathcal A$ of quantum observables $\hat a$ to a special class of generalized functions $a(X,\phi)$ such that the mean value $_{\hat \rho} =Tr(\hat \rho\hat a)$ is given by the formula $_{\hat \rho}= \int \limits_{0}^{2\pi}\int \limits_{-\infty}^{+\infty}w_{\hat \rho}(X,\phi)a(X,\phi)dXd\phi$. The class $\mathcal A$ includes all the symmetrized polynomials of canonical variables $\hat q$ and $\hat p$.Comment: 8 page

Comprehensive Disposal of Decommissioned Vehicles

The article concerns the final stage of the life cycle of vehicles (on the example of Russia). The purpose of the study is to develop an organizational scheme for the gradual creation of a unified system for the disposal of all types of vehicles that are out of service. The study included a legal, technical, and territorial analysis. For territorial analysis, statistical data were taken for the following types of transport: buses, trucks and cars. The result of the work is the division of recycling enterprises by recycling levels, namely, the use of classification A, B, C, D. Recycling centers organization is usually considered within the Federal districts, which will lead to the dispersion of recycling capacities throughout Russia. The Federal district will have a radical ring system of organizing recycling centers at different levels. The State should create a unified recycling system with the adoption of regulatory documents on the interaction of participants in the disposal of vehicles, it should involve commercial organizations in recycling activities in future. The prospects of the study suggest 3 options for the placement of warehouses and recycling centers for their effective operation and address the issue of recycling of highly specialized transport. © 2021 Elsevier B.V.. All rights reserved

On Hastings' counterexamples to the minimum output entropy additivity conjecture

Hastings recently reported a randomized construction of channels violating the minimum output entropy additivity conjecture. Here we revisit his argument, presenting a simplified proof. In particular, we do not resort to the exact probability distribution of the Schmidt coefficients of a random bipartite pure state, as in the original proof, but rather derive the necessary large deviation bounds by a concentration of measure argument. Furthermore, we prove non-additivity for the overwhelming majority of channels consisting of a Haar random isometry followed by partial trace over the environment, for an environment dimension much bigger than the output dimension. This makes Hastings' original reasoning clearer and extends the class of channels for which additivity can be shown to be violated.Comment: 17 pages + 1 lin