Related papers: Geometry of Generalized Depolarizing Channels
Polar coding over a class of binary discrete memoryless channels with channel knowledge at the encoder is studied. It is shown that polar codes achieve the capacity of convex and one-sided classes of symmetric channels.
We define and study the notion of quantum polarity, which is a kind of geometric Fourier transform between sets of positions and sets of momenta. Extending previous work of ours, we show that the orthogonal projections of the covariance…
The kinetics of the deposition of colloidal particles onto a solid surface is analytically studied. We take into account both the diffusion of particles from the bulk as well as the geometrical aspects of the layer of adsorbed particles. We…
Interferometric radio astronomy data require the effects of limited coverage in the Fourier plane to be accounted for via a deconvolution process. For the last 40 years this process, known as `cleaning', has been performed almost…
AdS black holes with planar event horizon topology play a central role in AdS/CFT holography, and particularly in its applications. Generalisations of the known planar black holes can be found by considering the Plebanski--Demianski…
We study the effect of a weakly driven atomic cloud's polarization distribution on its photon scattering lineshape. In doing this, we find three distinct polarization regimes. First, for dilute clouds, the polarization magnitude is…
We introduce a deformed product construction for simple polytopes in terms of lower-triangular block matrix representations. We further show how Gale duality can be employed for the construction and for the analysis of deformed products…
The cable equation describes the voltage in a straight cylindrical cable, this model has been employed to model electrical potential in dendrites and axons. However, sometimes this equation might give incorrect predictions for some…
The holographic correspondence predicts that certain strongly coupled quantum systems describe an emergent, higher-dimensional bulk spacetime in which excitations enjoy local dynamics. We consider a general holographic state dual to an…
We prove general type results for orthogonal modular varieties associated with the moduli of compact hyperk\"ahler manifolds of deformation generalised Kummer type ('deformation generalised Kummer varieties'). In particular, we consider…
We determine the possible gravitational wave polarizations in two general classes of teleparallel gravity theories, using the metric and symmetric teleparallel geometries. For this purpose we apply the Newman-Penrose formalism, and find…
A new approach to Nori's weak Lefschetz theorem is described. The new approach, which involves the dbar-method, avoids moving arguments and gives much stronger results. In particular, it is proved that if X and Y are connected smooth…
A generalized topology in a set $X$ is a collection $\text{Cov}_X$ of families of subsets of $X$ such that the triple $(X,\bigcup \text{Cov}_X,\text{Cov}_X)$ is a generalized topological space in the sense of Delfs and Knebusch. In this…
The apparently intractable shape of a fold in a compressed elastic film lying on a fluid substrate is found to have an exact solution. Such systems buckle at a nonzero wavevector set by the bending stiffness of the film and the weight of…
Motivated by a recent progress concerning quantum commuting and quantum tensor models of composed systems we investigate a notion of (generalized) unitary induced quantum channel. Using properties of Brown algebras we provide an equivalent…
A comprehensive graph theoretical and finite geometrical study of the commutation relations between the generalized Pauli operators of N-qudits is performed in which vertices/points correspond to the operators and edges/lines join commuting…
When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this…
We develop the fundamentals of a new theory of convex geometry -- which we call "broken line convex geometry". This is a theory of convexity where the ambient space is the rational tropicalization of a cluster variety, as opposed to an…
For a Coulomb system contained in a domain \Lambda, the dielectric susceptibility tensor \chi_{\Lambda} is defined as relating the average polarization in the system to a constant applied electric field, in the linear limit. According to…
In this paper we develop a theory of convexity for a free Abelian group M (the lattice of integer points), which we call theory of discrete convexity. We characterize those subsets X of the group M that could be call "convex". One property…