# Spatial entanglement of bosons in optical lattices.

@article{Cramer2013SpatialEO, title={Spatial entanglement of bosons in optical lattices.}, author={Marcus Cramer and Alain Bernard and Nicole Fabbri and Leonardo Fallani and Chiara Fort and Sara Rosi and Filippo Caruso and M. Inguscio and Martin Bodo Plenio}, journal={Nature communications}, year={2013}, volume={4}, pages={ 2161 } }

Entanglement is a fundamental resource for quantum information processing, occurring naturally in many-body systems at low temperatures. The presence of entanglement and, in particular, its scaling with the size of system partitions underlies the complexity of quantum many-body states. The quantitative estimation of entanglement in many-body systems represents a major challenge, as it requires either full-state tomography, scaling exponentially in the system size, or the assumption of…

## 55 Citations

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The approach provides analytical results for particular classes of mixed states of N qubits, and computable lower bounds to global, partial, or genuine multiparticle entanglement of any general state.

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This Letter establishes a data analysis method solving the closed set of equations relating tunneling currents and atom number dynamics, allowing for reliably recover the full covariance matrix, including off-diagonal terms representing coherent currents, and demonstrates how the obtained information about noncommuting observables allows one to quantify entanglement at finite temperature.

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This work analytically derives the lower bounds of broad families of entanglement criteria based on variances of arbitrary operators and lower bounding the best separable approximation and the generalized robustness only from measurements of first and second moments of the collective spin operator.

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