There is a local ring I of order 4, without identity for the multiplication, defined by generators and relations as $$\begin{aligned} I=\langle a,b \mid 2a=2b=0,\, a^2=b,\, \,ab=0 \rangle . \end{aligned}$$ We study recursive construction self-orthogonal codes over I. classify self orthogonal length n size $$2^n$$ (called here quasi self-dual or QSD) up to $$n=6.$$ In particular, we Type IV (QSD...

We consider a scenario where party, say, Alice prepares pure two-qubit (either maximally entangled or non-maximally entangled) state and sends one half of this to another distant Bob through qubit unital non-unital) channel. Finally, the shared is used as teleportation In scenario, we focus on characterizing set channels with respect final state's efficacy resource quantum (QT) in terms maximal...

We define natural A∞-transformations and construct A∞-category of A∞-functors. The notion of non-strict units in an A∞-category is introduced. The 2-category of (unital) A∞-categories, functors and transformations is described. The study of higher homotopy associativity conditions for topological spaces began with Stasheff’s article [Sta63, I]. In a sequel to this paper [Sta63, II] Stasheff def...

Assume that $A$‎, ‎$B$ are Banach algebras and that $m:Atimes Brightarrow B$‎, ‎$m^prime:Atimes Arightarrow B$ are bounded bilinear mappings‎. ‎We study the relationships between Arens regularity of $m$‎, ‎$m^prime$ and the Banach algebras $A$‎, ‎$B$‎. ‎For a Banach $A‎$‎-bimodule $B$‎, ‎we show that $B$ factors with respect to $A$ if and only if $B^{**}$ is unital as an $A^{**}‎$‎-module‎. ‎Le...

A unital embedded in a finite projective plane Π of order m# is a substructure of Π which forms a 2®(m$­1,m­1, 1) design. Several authors devoted their attention to the embedded unitals. The main aim is either to construct and investigate new classes of unitals, or to characterize some classes using group-theoretical or graphical properties [3, 6, 9, 18, 25]. In [3] we give some general results...

We analyze the structure of the subset of states generated by unital completely positive quantum maps, A witness that certifies that a state does not belong to the subset generated by a given map is constructed. We analyse the representations of positive maps and their relation to quantum Perron-Frobenius theory. PACS: 03.65.Bz, 03.67.-a, 03.65.Yz

Additivity of the Holevo capacity is proved for product channels, under the condition that one of the channels is in a certain class of unital qubit channels, with the other completely arbitrary. This qubit class includes the depolarizing channel. As a byproduct this proves that the Holevo bound is the ultimate information capacity of such qubit channels (assuming no prior entanglement between ...

Let $mathcal{A}$ be a Banach algebra and $mathcal{M}$ be a Banach $mathcal{A}$-bimodule. We say that a linear mapping $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{A} rightarrow mathcal{M}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{A}$. Giving some facts concerning general...