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Characterization of Entanglement in Continuous Variable Systems

Jan Sperling

Published Jan 1, 2011• 0 citations
Publisher

Abstract

Entanglement is a nonclassical correlation of compound quantum systems. We derive Separability-Eigenvalue-Equations. The solution of these equations delivers all observables for the determination of entanglement. On the other hand, it delivers entanglement quasi-probabilities. We conclude from negativities of such distributions, that no classical statistics can describe the state under study. For the quantification of entanglement we compare different entanglement measures. We also consider different kinds of entanglement and the relation to nonclassicality.

DOI
10.18453/rosdok_id00000886

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A unified characterization of continuous-variable quantum states is presented that gives general insight in their nonclassical features and, in particular, in their entanglement properties. Nonclassicality is characterized in terms of observable characteristic functions. Equivalently, the nonclassicality conditions are reformulated in terms of moments. The latter approach turns out to be a powerful tool for deriving a complete set of entanglement conditions for bipartite quantum systems, which are fully equivalent to the nonpositivity of the partially transposed density operator. The possibilities of observing the needed moments by balanced homodyne correlation measurements are analyzed.
We present how nonclassicality and entanglement can be characterized and detected efficiently for continuous variable systems. Of particular interest is the use of homodyne detections to measure quadrature amplitudes at minimum level to confirm nonclassicality and entanglement beyond Gaussian states. We introduce a systematic method for a functional form of uncertainty relations, which can be efficiently employed to experimentally detect non-Gaussian states comprehensively. Our approach for quantum correlations unifies a framework for quantum entanglement and quantum steering, which include the known results for Gaussian states and provides a better tool for non-Gaussian states than existing methods, e.g. entropic uncertainty relations.
Entanglement measures quantify nonclassical correlations present in a quantum system, but can be extremely difficult to calculate, even more so, when information on its state is limited. Here, we consider broad families of entanglement criteria that are based on variances of arbitrary operators and analytically derive the lower bounds these criteria provide for two relevant entanglement measures: the best separable approximation and the generalized robustness. This yields a practical method for quantifying entanglement in realistic experimental situations, in particular, when only few measurements of simple observables are available. As a concrete application of this method, we quantify bipartite and multipartite entanglement in spin-squeezed Bose-Einstein condensates of ∼500 atoms, by lower bounding the best separable approximation and the generalized robustness only from measurements of first and second moments of the collective spin operator.