Steering Maps and Their Application to Dimension-Bounded Steering.

The existence of quantum correlations that allow one party to steer the quantum state of another party is a counterintuitive quantum effect that was described at the beginning of the past century. Steering occurs if entanglement can be proven even though the description of the measurements on one party is not known, while the other side is characterized. We introduce the concept of steering maps, which allow us to unlock sophisticated techniques that were developed in regular entanglement detection and to use them for certifying steerability.

Steering bound entangled States: a counterexample to the stronger Peres conjecture.

Quantum correlations are at the heart of many applications in quantum information science and, at the same time, they form the basis for discussions about genuine quantum effects and their difference to classical physics. On one hand, entanglement theory provides the tools to quantify correlations in information processing and many results have been obtained to discriminate useful entanglement, which can be distilled to a pure form, from bound entanglement, being of limited use in many applications. On the other hand, for discriminating quantum phenomena from their classical counterparts, Schrödinger and Bell introduced the notions of steering and local hidden variable models.

Covariance matrices and the separability problem.

We propose a unifying approach to the separability problem using covariance matrices of locally measurable observables. From a practical point of view, our approach leads to strong entanglement criteria that allow us to detect the entanglement of many bound entangled states in higher dimensions and which are at the same time necessary and sufficient for two qubits. From a fundamental perspective, our approach leads to insights into the relations between several known entanglement criteria--such as the computable cross-norm and local uncertainty criteria--as well as their limitations.