3,687 research outputs found
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
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