Related papers: A class of positive atomic maps
We introduce the notion of one-sided mapping cones of positive linear maps between matrix algebras. These are convex cones of maps that are invariant under compositions by completely positive maps from either the left or right side. The…
Entanglement witnesses are observables which when measured, detect entanglement in a measured composed system. It is shown what kind of relations between eigenvectors of an observable should be fulfilled, to allow an observable to be an…
Classical matching theory can be defined in terms of matrices with nonnegative entries. The notion of Positive operator, central in Quantum Theory, is a natural generalization of matrices with nonnegative entries. Based on this point of…
Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is…
A new class of entanglement witnesses (EWs) called reduction type entanglement witnesses is introduced, which can detect some multi-qudit entangeled states including PPT ones with Hilbert space of dimension $d_{_{1}}\otimes…
The Gamma-class is a characteristic class for complex manifolds with transcendental coefficients. It defines an integral structure of quantum cohomology, or more precisely, an integral lattice in the space of flat sections of the quantum…
In this paper, a class of indecomposable positive finite rank elementary operators of order $(n,n)$ are constructed. This allows us to give a simple necessary and sufficient criterion for separability of pure states in bipartite systems of…
A scheme, where three atomic ensembles can be prepared in the states of the W-class via Raman type interaction of strong classical field and a projection measurement involved three single-photon detectors and two beamsplitters, are…
We reduce the question whether a given quantum mixed state is separable or entangled to the problem of existence of a certain full family of commuting normal matrices whose matrix elements are partially determined by components of the pure…
Entanglement is a key resource to demonstrate quantum advantage over classical strategies. Entanglement in quantum states is one of the most well-explored areas in quantum physics. However, a rigorous approach to understanding and detecting…
By putting together an abstract view on quantum mechanics and a quantum-optics picture of the interactions of an atom with light, we develop a corresponding set of C++ classes that set up the numerical analysis of an atom with an arbitrary…
We construct entangled states with positive partial transposes using indecomposable positive linear maps between matrix algebras. We also exhibit concrete examples of entangled states with positive partial transposes arising in this way,…
We construct a class of $3\otimes 3$ entangled edge states with positive partial transposes using indecomposable positive linear maps. This class contains several new types of entangled edge states with respect to the range dimensions of…
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…
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…
It is proven that a certain class of positive maps in the matrix algebra $M_n$ consists of optimal maps, i.e. maps from which one cannot subtract any completely positive map without loosing positivity. This class provides a generalization…
We obtain a new inequality for arbitrary Hermitian matrices. We describe particular linear maps called the matrix portrait of arbitrary NxN matrices. The maps are obtained as analogs of partial tracing of density matrices of multipartite…
We develop a strong and computationally simple entanglement criterion. The criterion is based on an elementary positive map Phi which operates on state spaces with even dimension N >= 4. It is shown that Phi detects many entangled states…
A novel algebra underlying integrable systems is shown to generate and unify a large class of quantum integrable models with given $R$-matrix, through reductions of an ancestor Lax operator and its different realizations. Along with known…
The problem of determining whether a given quantum state is entangled lies at the heart of quantum information processing, which is known to be an NP-hard problem in general. Despite the proposed many methods such as the positive partial…