Entanglement quantification through local observable correlations

We present a significantly improved scheme of entanglement detection inspired by local uncertainty relations for a system consisting of two qubits. Developing the underlying idea of local uncertainty relations, namely correlations, we demonstrate that it is possible to define a measure which is invariant under local unitary transformations and which is based only on local measurements. It is quite simple to implement experimentally and it allows entanglement quantification in a certain range for mixed states and exactly for pure states, without first obtaining full knowledge (e.g., through tomography) of the state.

Figure 1

Bounds for $G$ when plotted over the concurrence. See text for more details.

Figure 2

Simulation results of measuring $G$ for some mixed states. The upper figure is for states with a purity of $\mathrm{Tr}\left({\widehat{\rho }}^2\right)=0.46\pm 0.005$ and the lower figure is for states with $\mathrm{Tr}\left({\widehat{\rho }}^2\right)=0.5\pm 0.005$.