Necessary and sufficient conditions for bipartite entanglement

Necessary and sufficient conditions for bipartite entanglement are derived, which apply to arbitrary Hilbert spaces. Motivated by the concept of witnesses, optimized entanglement inequalities are formulated solely in terms of arbitrary Hermitian operators, which makes them useful for applications in experiments. The needed optimization procedure is based on a separability eigenvalue problem, whose analytical solutions are derived for a special class of projection operators. For general Hermitian operators, a numerical implementation of entanglement tests is proposed. It is also shown how to identify bound entangled states with positive partial transposition.Comment: 7 pages, 2 figur

Sharing the Burden of Collective Security in the European Union. Research Note

This article compares European Union (EU) burden-sharing in security governance distinguishing between assurance, prevention, protection, and compellence policies. We employ joint-product models and examine the variation in the level of publicness, the asymmetry of the distribution of costs and benefits, and aggregation technologies in each policy domain. Joint-product models predict equal burden sharing for protection and assurance because of their respective weakest-link and summation aggregation technologies with symmetric costs. Prevention is also characterized by the technology of summation, but asymmetry of costs implies uneven burden-sharing. Uneven burden-sharing is predicted for compellence because it has the largest asymmetry of costs and a best-shot aggregation technology. Evaluating burden-sharing relative to a country?s ability to contribute, Kendall tau-tests examine the rank-correlation between security burden and the capacity of EU member states. These tests show that the smaller EU members disproportionately shoulder the costs of assurance and protection; wealthier EU members carry a somewhat disproportionate burden in the provision of prevention, and larger EU members in the provision of compellence. When analyzing contributions relative to expected benefits, asymmetric marginal costs can largely explain uneven burden-sharing. The main conclusion is that the aggregated burden of collective security governance in the EU is shared quite evenly

Convex ordering and quantification of quantumness

The characterization of physical systems requires a comprehensive understanding of quantum effects. One aspect is a proper quantification of the strength of such quantum phenomena. Here, a general convex ordering of quantum states will be introduced which is based on the algebraic definition of classical states. This definition resolves the ambiguity of the quantumness quantification using topological distance measures. Classical operations on quantum states will be considered to further generalize the ordering prescription. Our technique can be used for a natural and unambiguous quantification of general quantum properties whose classical reference has a convex structure. We apply this method to typical scenarios in quantum optics and quantum information theory to study measures which are based on the fundamental quantum superposition principle.Comment: 9 pages, 2 figures, revised version; published in special issue "150 years of Margarita and Vladimir Man'ko

Entanglement and phase properties of noisy N00N states

Quantum metrology and quantum information necessitate a profound study of suitable states. Attenuations induced by free-space communication links or fluctuations in the generation of such states limit the quantum enhancement in possible applications. For this reason we investigate quantum features of mixtures of so-called N00N states propagating in atmospheric channels. First, we show that noisy N00N states can still yield a phase resolution beyond classical limitations. Second, we identify entanglement of noisy N00N states after propagation in fluctuating loss channels. To do so, we apply the partial transposition criterion. Our theoretical analysis formulates explicit bounds which are indispensable for experimental verification of quantum entanglement and applications in quantum metrology

Verifying continuous-variable entanglement in finite spaces

Starting from arbitrary Hilbert spaces, we reduce the problem to verify entanglement of any bipartite quantum state to finite dimensional subspaces. Hence, entanglement is a finite dimensional property. A generalization for multipartite quantum states is also given.Comment: 4 page

Representation of entanglement by negative quasi-probabilities

Any bipartite quantum state has quasi-probability representations in terms of separable states. For entangled states these quasi-probabilities necessarily exhibit negativities. Based on the general structure of composite quantum states, one may reconstruct such quasi-propabilities from experimental data. Because of ambiguity, the quasi-probabilities obtained by the bare reconstruction are insufficient to identify entanglement. An optimization procedure is introduced to derive quasi-probabilities with a minimal amount of negativity. Negativities of optimized quasi-probabilities unambiguously prove entanglement, their positivity proves separability.Comment: 9 pages, 2 figures; An optimization procedure for the quasi-probabilities has been adde

Quantum Correlations from the Conditional Statistics of Incomplete Data

We study, in theory and experiment, the quantum properties of correlated light fields measured with click-counting detectors providing incomplete information on the photon statistics. We establish a correlation parameter for the conditional statistics, and we derive the corresponding nonclassicality criteria for detecting conditional quantum correlations. Classical bounds for Pearson's correlation parameter are formulated that allow us, once they are violated, to determine nonclassical correlations via the joint statistics. On the one hand, we demonstrate nonclassical correlations in terms of the joint click statistics of light produced by a parametric down conversion source. On the other hand, we verify quantum correlations of a heralded, split single-photon state via the conditional click statistics together with a generalization to higher-order moments. We discuss the performance of the presented nonclassicality criteria to successfully discern joint and conditional quantum correlations. Remarkably, our results are obtained without making any assumptions on the response function, quantum efficiency, and dark-count rate of the photodetectors