4,642 research outputs found
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
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
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
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
Benchmarking of Gaussian boson sampling using two-point correlators
Gaussian boson sampling is a promising scheme for demonstrating a quantum
computational advantage using photonic states that are accessible in a
laboratory and, thus, offer scalable sources of quantum light. In this
contribution, we study two-point photon-number correlation functions to gain
insight into the interference of Gaussian states in optical networks. We
investigate the characteristic features of statistical signatures which enable
us to distinguish classical from quantum interference. In contrast to the
typical implementation of boson sampling, we find additional contributions to
the correlators under study which stem from the phase dependence of Gaussian
states and which are not observable when Fock states interfere. Using the first
three moments, we formulate the tools required to experimentally observe
signatures of quantum interference of Gaussian states using two outputs only.
By considering the current architectural limitations in realistic experiments,
we further show that a statistically significant discrimination between quantum
and classical interference is possible even in the presence of loss, noise, and
a finite photon-number resolution. Therefore, we formulate and apply a
theoretical framework to benchmark the quantum features of Gaussian boson
sampling under realistic conditions
- …