Related papers: Infinite dimensional generalizations of Choi's the…
In this note, we define a bounded variant on the Hilbert projective metric on an infinite dimensional space $E$ and study the contraction properties of the projective maps associated with positive linear operators on $E$. More precisely, we…
We present a simple, dimension-independent criterion which guarantees that some quantum channel $\Phi$ is divisible, i.e. that there exists a non-trivial factorization $\Phi=\Phi_1\Phi_2$. The idea is to first define an "elementary" channel…
Quantum states that remain separable (i.e., not entangled) under any global unitary transformation are known as absolutely separable and form a convex set. Despite extensive efforts, the complete characterization of this set remains largely…
We present a method for the determination of the completely positive (CP) map describing a physical device based on random preparation of the input states, random measurements at the output, and maximum-likelihood principle. In the…
This article is to give an infinite dimensional analogue of a result of Choi and Effros. We say that an (not necessarily unital) operator system $T$ is \emph{dualizable} if one can find an equivalent dual matrix norm on the dual space $T^*$…
We introduce a class of linear maps irreducibly covariant with respect to the finite group generated by the Weyl operators. This group provides a direct generalization of the quaternion group. In particular, we analyze the irreducibly…
Quantum supermaps are a higher-order generalization of quantum maps, taking quantum maps to quantum maps. It is known that any completely positive, trace non-increasing (CPTNI) map can be performed as part of a quantum measurement. By…
We investigate a two-parameter family of linear maps on matrix algebras, constructed as diagonal perturbations of classical Tomiyama maps. Employing the Choi matrix method alongside block-positivity techniques, we derive explicit necessary…
The classical as well as non commutative Korovkin-type theorems deal with convergence of positive linear maps with respect to modes of convergences such as norm convergence and weak operator convergence. In this article, Korovkin-type…
We analyse possibility to extend a quantum operation (sub-unital normal CP linear map on the algebra $B(H)$ of bounded operators on a separable Hilbert space $H$) to the space of all operators on $H$ relatively bounded w.r.t. a given…
We study a class of quantum channels describing a quantum system, split into the direct sum of an excited and a ground sector, undergoing a one-way transfer of population from the former to the latter; this construction, which provides a…
In this paper, we present the necessary and sufficient conditions of separability for bipartite pure states in infinite dimensional Hilbert spaces. Let $M$ be the matrix of the amplitudes of $\ket\psi$, we prove $M$ is a compact operator.…
We consider complete positivity of dynamics regarding subsystems of an open composite quantum system, which is subject of a completely positive dynamics. By "completely positive dynamics", we assume the dynamical maps called the completely…
Quantum channels, a subset of quantum maps, describe the unitary and non-unitary evolution of quantum systems. We study a generalization of the concept of Pauli maps to the case of multipartite high dimensional quantum systems through the…
Characterizing those quantum channels that correspond to Markovian time evolutions is an open problem in quantum information theory, even different notions of quantum Markovianity exist. One such notion is that of infinitesimal Markovian…
Entanglement breaking (EB) channels, as completely positive and trace-preserving linear operators, sever the entanglement between the input system and other systems. In the realm of infinite-dimensional systems, a related concept known as…
We analyze the geometry of positive and completely positive, trace preserving Pauli maps that are fully determined by up to two distinct parameters. This includes five classes of symmetric and non-invertible Pauli channels. Using the…
A geometric characterization is given for invertible quantum measurement maps. Denote by ${\mathcal S}(H)$ the convex set of all states (i.e., trace-1 positive operators) on Hilbert space $H$ with dim$H\leq \infty$, and $[\rho_1, \rho_2]$…
While algebraic derivations establish theoretical limits for quantum cloning, practical implementations require explicit operator representations that are often unavailable analytically. We present a computational framework that…
The problem of entanglement detection is a long standing problem in quantum information theory. One of the primary procedures of detecting entanglement is to find the suitable positive but non-completely positive maps. Here we try to give a…