Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems

The effect of quantum steering describes a possible action at a distance via local measurements. Whereas many attempts on characterizing steerability have been pursued, answering the question as to whether a given state is steerable or not remains a difficult task. Here, we investigate the applicability of a recently proposed method for building steering criteria from generalized entropic uncertainty relations. This method works for any entropy which satisfy the properties of (i) (pseudo-) additivity for independent distributions; (ii) state independent entropic uncertainty relation (EUR); and (iii) joint convexity of a corresponding relative entropy. Our study extends the former analysis to Tsallis and R\'enyi entropies on bipartite and tripartite systems. As examples, we investigate the steerability of the three-qubit GHZ and W states.Comment: 27 pages, 8 figures. Published version. Title change

Nonlinear entanglement witnesses, covariance matrices and the geometry of separable states

Entanglement witnesses provide a standard tool for the analysis of entanglement in experiments. We investigate possible nonlinear entanglement witnesses from several perspectives. First, we demonstrate that they can be used to show that the set of separable states has no facets. Second, we give a new derivation of nonlinear witnesses based on covariance matrices. Finally, we investigate extensions to the multipartite case.Comment: 12 pages, 2 figures, for the proceedings of DICE2006 in Piombino (Italy

Entanglement Detection in the Stabilizer Formalism

We investigate how stabilizer theory can be used for constructing sufficient conditions for entanglement. First, we show how entanglement witnesses can be derived for a given state, provided some stabilizing operators of the state are known. These witnesses require only a small effort for an experimental implementation and are robust against noise. Second, we demonstrate that also nonlinear criteria based on uncertainty relations can be derived from stabilizing operators. These criteria can sometimes improve the witnesses by adding nonlinear correction terms. All our criteria detect states close to Greenberger-Horne-Zeilinger states, cluster and graph states. We show that similar ideas can be used to derive entanglement conditions for states which do not fit the stabilizer formalism, such as the three-qubit W state. We also discuss connections between the witnesses and some Bell inequalities.Comment: 15 pages including 2 figures, revtex4; typos corrected, presentation improved; to appear in PR

Armut im Alter – Ursachenanalyse und eine Projektion für das Jahr 2023

Several factors bring about a rise in old age poverty in Germany, especially in East Germany. Using data from the German Socio-economic Panel (SOEP) we examine causes and extent of old age poverty in Germany. We begin our inquiry with a cross section regression in order to determine the impact of several factors on retirement incomes in Germany. In the second step we perform an income projection of today’s 50 to 55 year-old people for the year 2023. In doing so, we take into account different sources of income, including several forms of capital income and the calculated rent of owner-occupied houses and flats. We find a significant rise in old age poverty especially in East Germany as a consequence of rising unemployment after the German unification.old age poverty, pension, old age income

Entanglement and nonclassical properties of hypergraph states

Hypergraph states are multi-qubit states that form a subset of the locally maximally entangleable states and a generalization of the well--established notion of graph states. Mathematically, they can conveniently be described by a hypergraph that indicates a possible generation procedure of these states; alternatively, they can also be phrased in terms of a non-local stabilizer formalism. In this paper, we explore the entanglement properties and nonclassical features of hypergraph states. First, we identify the equivalence classes under local unitary transformations for up to four qubits, as well as important classes of five- and six-qubit states, and determine various entanglement properties of these classes. Second, we present general conditions under which the local unitary equivalence of hypergraph states can simply be decided by considering a finite set of transformations with a clear graph-theoretical interpretation. Finally, we consider the question whether hypergraph states and their correlations can be used to reveal contradictions with classical hidden variable theories. We demonstrate that various noncontextuality inequalities and Bell inequalities can be derived for hypergraph states.Comment: 29 pages, 5 figures, final versio

Efficient kk-separability criteria for mixed multipartite quantum states

We investigate classification and detection of entanglement of multipartite quantum states in a very general setting, and obtain efficient $k$-separability criteria for mixed multipartite states in arbitrary dimensional quantum systems. These criteria can be used to distinguish $n-1$ different classes of multipartite inseparable states and can detect many important multipartite entangled states such as GHZ states, W states, anti W states, and mixtures thereof. They detect $k$-nonseparable $n$-partite quantum states which have previously not been identified. Here $k=2,3,\cdots,n$. No optimization or eigenvalue evaluation is needed, and our criteria can be evaluated by simple computations involving components of the density matrix. Most importantly, they can be implemented in today's experiments by using at most $\mathcal{O}(n^2)$ local measurements.Comment: 6 pages, 4 figure

Entanglement verification for quantum key distribution systems with an underlying bipartite qubit-mode structure

We consider entanglement detection for quantum key distribution systems that use two signal states and continuous variable measurements. This problem can be formulated as a separability problem in a qubit-mode system. To verify entanglement, we introduce an object that combines the covariance matrix of the mode with the density matrix of the qubit. We derive necessary separability criteria for this scenario. These criteria can be readily evaluated using semidefinite programming and we apply them to the specific quantum key distribution protocol.Comment: 6 pages, 2 figures, v2: final versio

Two-setting Bell Inequalities for Graph States

We present Bell inequalities for graph states with high violation of local realism. In particular, we show that there is a two-setting Bell inequality for every nontrivial graph state which is violated by the state at least by a factor of two. These inequalities are facets of the convex polytope containing the many-body correlations consistent with local hidden variable models. We first present a method which assigns a Bell inequality for each graph vertex. Then for some families of graph states composite Bell inequalities can be constructed with a violation of local realism increasing exponentially with the number of qubits. We also suggest a systematic way for obtaining Bell inequalities with a high violation of local realism for arbitrary graphs.Comment: 8 pages including 2 figures, revtex4; minor change