Related papers: Positive maps, states, entanglement and all that; …
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…
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In…
A necessary and sufficient condition for 1-distillability is formulated in terms of decomposable positive maps. As an application we provide insight into why all states violating the reduction criterion map are distillable and demonstrate…
We extend the theory of decomposable maps by giving a detailed description of k-positive maps. A relation between transposition and modular theory is established. The structure of positive maps in terms of modular theory (the generalized…
Bhat characterizes the family of linear maps defined on $B(\mathcal{H})$ which preserve unitary conjugation. We generalize this idea and study the maps with a similar equivariance property on finite-dimensional matrix algebras. We show that…
Entanglement detection is an important problem in quantum information theory because quantum entanglement is a key resource in quantum information processing. Realignment criteria is a powerful tool for detection of entangled states in…
Second degree polynomial Heisenberg algebras are realized through the harmonic oscillator Hamiltonian, together with two deformed ladder operators chosen as the third powers of the standard annihilation and creation operators. The…
Given two sets of quantum states {A_1, ..., A_k} and {B_1, ..., B_k}, represented as sets of density matrices, necessary and sufficient conditions are obtained for the existence of a physical transformation T, represented as a…
In quantum mechanics, often it is important for the representation of quantum system to study the structure-preserving bijective maps of the quantum system. Such maps are also called isomorphisms or automorphisms. In this note, using the…
Complete positivity of quantum dynamics is often viewed as a litmus test for physicality, yet it is well known that correlated initial states need not give rise to completely positive evolutions. This observation spurred numerous…
We show that the geometry of the set of quantum states plays a crucial role in the behavior of entanglement in different physical systems. More specifically it is shown that singular points at the border of the set of unentangled states…
We present a survey on mathematical topics relating to separable states and entanglement witnesses. The convex cone duality between separable states and entanglement witnesses is discussed and later generalized to other families of…
We investigate the evolution of open quantum systems in the presence of initial correlations with an environment. Here the standard formalism of describing evolution by completely positive trace preserving (CPTP) quantum operations can fail…
We study emerging notions of quantum correlations in compound systems. Based on different definitions of quantumness in individual subsystems, we investigate how they extend to the joint description of a composite system. Especially, we…
We prove several new transversality results for formal CR maps between formal real hypersurfaces in complex space. Both cases of finite and infinite type hypersurfaces are tackled in this note.
In this paper, we introduce a new positivity notion for curvature of Riemannian manifolds and obtain characterizations for spherical space forms and the complex projective space $\mathbb{C}\mathbb{P}^n$.
In this paper we establish the equivalence of solutions between Schr\"odinger map into $\mathbb{S}^2$ or $ \mathbb{H}^2$ and their associated gauge invariant Schr\"odinger equations. We also establish the existence of global weak solutions…
We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.
We obtain restrictions on the rational homotopy types of mapping spaces and of classifying spaces of homotopy automorphisms by means of the theory of positive weight decompositions. The theory applies, in particular, to connected components…
We extend fundamental inequalities related to the canonical map of surfaces of general type to positive characteristic. Next, we classify surfaces on the Noether lines, i.e., even and odd Horikawa surfaces, in positive characteristic. We…