The Hilbertian Tensor Norm and Entangled Two-Prover Games

We study tensor norms over Banach spaces and their relations to quantum information theory, in particular their connection with two-prover games. We consider a version of the Hilbertian tensor norm $\gamma_2$ and its dual $\gamma_2^*$ that allow us to consider games with arbitrary output alphabet sizes. We establish direct-product theorems and prove a generalized Grothendieck inequality for these tensor norms. Furthermore, we investigate the connection between the Hilbertian tensor norm and the set of quantum probability distributions, and show two applications to quantum information theory: firstly, we give an alternative proof of the perfect parallel repetition theorem for entangled XOR games; and secondly, we prove a new upper bound on the ratio between the entangled and the classical value of two-prover games.Comment: 33 pages, some of the results have been obtained independently in arXiv:1007.3043v2, v2: an error in Theorem 4 has been corrected; Section 6 rewritten, v3: completely rewritten in order to improve readability; title changed; references added; published versio

Highly efficient separation of actinides from lanthanides by a phenanthroline-derived bis-triazine ligand

The synthesis, lanthanide complexation, and solvent ex- traction of actinide(III) and lanthanide(III) radiotracers from nitric acid solutions by a phenanthroline-derived quadridentate bis-triazine ligand are described. The ligand separates Am(III) and Cm(III) from the lanthanides with remarkably high efficiency, high selectivity, and fast extraction kinetics compared to its 2,2'-bipyridine counterpart. Structures of the 1:2 bis-complexes of the ligand with Eu(III) and Yb(III) were elucidated by X-ray crystallography and force field calculations, respec-tively. The Eu(III) bis-complex is the first 1:2 bis-complex of a quadridentate bis-triazine ligand to be characterized by crystallography. The faster rates of extraction were verified by kinetics measurements using the rotating membrane cell technique in several diluents. The improved kinetics of metal ion extraction are related to the higher surface activity of the ligand at the phase interface. The improvement in the ligand's properties on replacing the bipyridine unit with a phenanthroline unit far exceeds what was anticipated based on ligand design alone

A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations

We are interested in the problem of characterizing the correlations that arise when performing local measurements on separate quantum systems. In a previous work [Phys. Rev. Lett. 98, 010401 (2007)], we introduced an infinite hierarchy of conditions necessarily satisfied by any set of quantum correlations. Each of these conditions could be tested using semidefinite programming. We present here new results concerning this hierarchy. We prove in particular that it is complete, in the sense that any set of correlations satisfying every condition in the hierarchy has a quantum representation in terms of commuting measurements. Although our tests are conceived to rule out non-quantum correlations, and can in principle certify that a set of correlations is quantum only in the asymptotic limit where all tests are satisfied, we show that in some cases it is possible to conclude that a given set of correlations is quantum after performing only a finite number of tests. We provide a criterion to detect when such a situation arises, and we explain how to reconstruct the quantum states and measurement operators reproducing the given correlations. Finally, we present several applications of our approach. We use it in particular to bound the quantum violation of various Bell inequalities.Comment: 33 pages, 2 figure

Interaction of 6,6′′-bis(5,5,8,8-tetramethyl-5,6,7,8-tetrahydro-1,2,4-benzotriazin-3-yl)-2,2′:6′,2′′-terpyridine (CyMe4-BTTP) with some trivalent ions such as lanthanide(iii) ions and americium(iii)

The new ligand 6,6 ''-bis(5,5,8,8-tetramethyl-5,6,7,8-tetrahydro-1,2,4-benzotriazin-3-yl)2,2':6 ',2 ''-terpyridine (CyMe4-BTTP) has been synthesized in 4 steps from 2,2':6',2 ''-terpyridine. Detailed NMR and mass spectrometry studies indicate that the ligand forms 1 : 2 complexes with lanthanide(III) perchlorates where the aliphatic rings are conformationally constrained whereas 1 : 1 complexes are formed with lanthanide(III) nitrates where the rings are conformationally mobile. An optimized structure of the 1 : 2 solution complex with Yb(III) was obtained from the relative magnitude of the induced paramagnetic shifts. X-Ray crystallographic structures of the ligand and of its 1 : 1 complex with Y(III) were also obtained. The NMR and mass spectra of [Pd(CyMe4-BTTP)](n)(2n+) are consistent with a dinuclear double helical structure (n = 2). In the absence of a phase-modifier, CyMe4-BTTP in n-octanol showed a maximum distribution coefficient of Am(III) of 0.039 (+/-20%) and a maximum separation factor of Am(III) over Eu(III) of 12.0 from nitric acid. The metal(III) cations are extracted as the 1 : 1 complex from nitric acid. The generally low distribution coefficients observed compared with the BTBPs arise because the 1 : 1 complex of CyMe4-BTTP is considerably less hydrophobic than the 1 : 2 complexes formed by the BTBPs. In M(BTTP)(3+) complexes, there is a competition between the nitrate ions and the ligand for the complexation of the metal

Pr parations,propri t s de surface et activit catalytique du carbure de tungst(ne

SIGLEBSE B222929B / UCL - Université Catholique de LouvainBEBelgiu