205 research outputs found
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 -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 -separability
criteria for mixed multipartite states in arbitrary dimensional quantum
systems. These criteria can be used to distinguish 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 -nonseparable -partite quantum states which have
previously not been identified. Here . 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
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
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