Marcin Marciniak

On a characterization of positive maps

Drawing on results of Choi, Stormer and Woronowicz, we present a nearly complete characterization of certain important classes of positive maps. In particular, we construct a general class of positive linear maps acting between two matrix algebras B(H) and B(K), where H and K are finite-dimensional Hilbert spaces. It turns out that elements of this class are characterized by operators from the dual cone of the set of all separable states on B(H ⊗ K). Subsequently, the relation between entanglements and positive maps is described. Finally, a new characterization of the cone B(H) + ⊗ B(K) + is given.

Rank properties of exposed positive maps

Let 𝒦 and ℋ be finite dimensional Hilbert spaces and let denote the cone of all positive linear maps acting from into . We show that each map of the form φ(X) = AXA* or φ(X) = AX T A* is an exposed point of . It is done by careful analysis of rank properties of these maps.

On extremal positive maps acting between type I factors

The paper is devoted to the problem of classification of extremal positive maps acting between

Operator space approach to steering inequality

B(K)

On quantum Lyapunov exponents

and

Merging of positive maps: A construction of various classes of positive maps on matrix algebras

B(H)

Generalizing Choi-Like Maps

where

Multiple noncommutative tori as quantum symmetry groups

K

ON THE STRUCTURE OF POSITIVE MAPS BETWEEN MATRIX ALGEBRAS

and

k-DECOMPOSABILITY OF POSITIVE MAPS

H