Witnessing random unitary and projective quantum channels: Complementarity between separable and maximally entangled states

Modern applications in quantum computation and quantum communication require the precise characterization of quantum states and quantum channels. In practice, this means that one has to determine the quantum capacity of a physical system in terms of measurable quantities. Witnesses, if properly constructed, succeed in performing this task. We derive a method that is capable to compute witnesses for identifying deterministic evolutions and measurement-induced collapse processes. At the same time, applying the Choi-Jamiolkowski isomorphism, it uncovers the entanglement characteristics of bipartite quantum states. Remarkably, a statistical mixture of unitary evolutions is mapped onto mixtures of maximally entangled states, and classical separable states originate from genuine quantum-state reduction maps. Based on our treatment we are able to witness these opposing attributes at once and, furthermore, obtain an insight into their different geometric structures. The complementarity is further underpinned by formulating a complementary Schmidt decomposition of a state in terms of maximally entangled states and discrete Fourier-transformed Schmidt coefficients.Comment: close to published versio

Instantons on conical half-flat 6-manifolds

We present a general procedure to construct 6-dimensional manifolds with SU(3)-structure from SU(2)-structure 5-manifolds. We thereby obtain half-flat cylinders and sine-cones over 5-manifolds with Sasaki-Einstein SU(2)-structure. They are nearly Kahler in the special case of sine-cones over Sasaki-Einstein 5-manifolds. Both half-flat and nearly Kahler 6-manifolds are prominent in flux compactifications of string theory. Subsequently, we investigate instanton equations for connections on vector bundles over these half-flat manifolds. A suitable ansatz for gauge fields on these 6-manifolds reduces the instanton equation to a set of matrix equations. We finally present some of its solutions and discuss the instanton configurations obtained this way.Comment: 1+32 pages, 1 figure, v2: 6 references added, v2 accepted for publication in JHE

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

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

Gene Flow Between Great Lakes Region Populations of the Canadian Tiger Swallowtail Butterfly, \u3ci\u3ePapilio Canadensis\u3c/i\u3e, Near the Hybrid Zone With \u3ci\u3eP. Glaucus\u3c/i\u3e (Lepidoptera: Papilionidae)

Papilio canadensis were sampled from three locations on either side of Lake Michigan to study gene flow near and through a butterfly hybrid zone. Allele frequencies at four polymorphic enzyme loci, as indicated by allozyme electrophoresis, were similar in all samples. Values for FST were close to zero, indicating that gene flow is high among these populations, even when separated by Lake Michigan. We developed a mitochondrial DNA marker with diagnostic differences between P. canadensis and its parapatric sister species Papilio glaucus, based on PCR-RFLP. P. glaucus haplotypes of this mtDNA marker and P. glaucus alleles of a diagnostic allozyme locus (PGD) were found in P. canadensis populations sampled in Michigan’s Lower Peninsula but not in the Upper Peninsula or Northern Minnesota. The presence of P. glaucus alleles in P. canadensis populations could be due to introgression through hybridization, or could be remnants of a P. glaucus population that was inundated by an influx of P. canadensis alleles

Presurgical thalamic hubness predicts surgical outcome in temporal lobe epilepsy.

OBJECTIVE: To characterize the presurgical brain functional architecture presented in patients with temporal lobe epilepsy (TLE) using graph theoretical measures of resting-state fMRI data and to test its association with surgical outcome. METHODS: Fifty-six unilateral patients with TLE, who subsequently underwent anterior temporal lobectomy and were classified as obtaining a seizure-free (Engel class I, n = 35) vs not seizure-free (Engel classes II-IV, n = 21) outcome at 1 year after surgery, and 28 matched healthy controls were enrolled. On the basis of their presurgical resting-state functional connectivity, network properties, including nodal hubness (importance of a node to the network; degree, betweenness, and eigenvector centralities) and integration (global efficiency), were estimated and compared across our experimental groups. Cross-validations with support vector machine (SVM) were used to examine whether selective nodal hubness exceeded standard clinical characteristics in outcome prediction. RESULTS: Compared to the seizure-free patients and healthy controls, the not seizure-free patients displayed a specific increase in nodal hubness (degree and eigenvector centralities) involving both the ipsilateral and contralateral thalami, contributed by an increase in the number of connections to regions distributed mostly in the contralateral hemisphere. Simulating removal of thalamus reduced network integration more dramatically in not seizure-free patients. Lastly, SVM models built on these thalamic hubness measures produced 76% prediction accuracy, while models built with standard clinical variables yielded only 58% accuracy (both were cross-validated). CONCLUSIONS: A thalamic network associated with seizure recurrence may already be established presurgically. Thalamic hubness can serve as a potential biomarker of surgical outcome, outperforming the clinical characteristics commonly used in epilepsy surgery centers

Instantons on sine-cones over Sasakian manifolds

We investigate instantons on sine-cones over Sasaki-Einstein and 3-Sasakian manifolds. It is shown that these conical Einstein manifolds are K"ahler with torsion (KT) manifolds admitting Hermitian connections with totally antisymmetric torsion. Furthermore, a deformation of the metric on the sine-cone over 3-Sasakian manifolds allows one to introduce a hyper-K"ahler with torsion (HKT) structure. In the large-volume limit these KT and HKT spaces become Calabi-Yau and hyper-K"ahler conifolds, respectively. We construct gauge connections on complex vector bundles over conical KT and HKT manifolds which solve the instanton equations for Yang-Mills fields in higher dimensions.Comment: 1+15 pages, 2 figure

Understanding seed systems and strengthening seed security

This paper provides background information on seed systems and seed relief interventions for participants at the Workshop on Effective and Sustainable Seed Relief Activities, Rome, 26–28 May 2003. In this paper we review the rationale for and goals of seed aid (section II) and provide an overview of seed systems, with particular attention to the “local” or “informal” seed system that provides most farmers with seeds most of the time (section III). In section IV, the parameters of seed security are discussed, including the distinctions between availability, access, and utilization (or quality) attributes. Acute and chronic emergency situations are also described. In section V, lessons learned from experience in the field, particularly in Africa, are summarized and discussed, and in section VI, current response options are described and compared, focusing in particular on direct seed distribution and seed fairs and vouchers. Finally, some major challenges for moving ahead are considered in section VII