Covariance matrices and the separability problem

We propose a unifying approach to the separability problem using covariance matrices of locally measurable observables. From a practical point of view, our approach leads to strong entanglement criteria that allow to detect the entanglement of many bound entangled states in higher dimensions and which are at the same time necessary and sufficient for two qubits. From a fundamental perspective, our approach leads to insights into the relations between several known entanglement criteria -- such as the computable cross norm and local uncertainty criteria -- as well as their limitations.Comment: 4 pages, no figures; v3: final version to appear in PR

Classical Tensors and Quantum Entanglement I: Pure States

The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a flat Riemannian metric tensor while the imaginary part represents a symplectic two-form. The immersion of classical manifolds in the complex projective space associated with the Hilbert space allows to pull-back tensor fields related to previous ones, via the immersion map. This makes available, on these selected manifolds of states, methods of usual Riemannian and symplectic geometry. Here we consider these pulled-back tensor fields when the immersed submanifold contains separable states or entangled states. Geometrical tensors are shown to encode some properties of these states. These results are not unrelated with criteria already available in the literature. We explicitly deal with some of these relations.Comment: 16 pages, 1 figure, to appear in Int. J. Geom. Meth. Mod. Phy

Classical Tensors and Quantum Entanglement II: Mixed States

Invariant operator-valued tensor fields on Lie groups are considered. These define classical tensor fields on Lie groups by evaluating them on a quantum state. This particular construction, applied on the local unitary group U(n)xU(n), may establish a method for the identification of entanglement monotone candidates by deriving invariant functions from tensors being by construction invariant under local unitary transformations. In particular, for n=2, we recover the purity and a concurrence related function (Wootters 1998) as a sum of inner products of symmetric and anti-symmetric parts of the considered tensor fields. Moreover, we identify a distinguished entanglement monotone candidate by using a non-linear realization of the Lie algebra of SU(2)xSU(2). The functional dependence between the latter quantity and the concurrence is illustrated for a subclass of mixed states parametrized by two variables.Comment: 23 pages, 4 figure

The intrinsic fluorescence of FAD and its application in analytical chemistry: a review

This review (with 106 references) mainly deals with the analytical applications of flavin-adenine dinucleotide (FAD) fluorescence. In the first section, the spectroscopic properties of this compound are reviewed at the light of his different acid-base, oxidation and structural forms; the chemical and spectroscopic properties of flavin mononucleotide (FMN) and other flavins will be also briefly discussed. The second section discusses how the properties of FAD fluorescence changes in flavoenzymes (FvEs), again considering the different chemical and structural forms; the glucose oxidase (GOx) and the choline oxidase (ChOx) cases will be commented. Since almost certainly the most reported analytical application of FAD fluorescence is as an auto-indicator in enzymatic methods catalysed by FvE oxidoreductases, it is important to know how the concentrations of the different forms of FAD changes along the reaction and, consequently, the fluorescence and the analytical signals. An approach to do this will be presented in section 3. The fourth part of the paper compiles the analytical applications which have been reported until now based in these fluorescence properties. Finally, some suggestions about tentative future research are also given