Experimental Estimation of Entanglement at the Quantum Limit

Entanglement is the central resource of quantum information processing and the precise characterization of entangled states is a crucial issue for the development of quantum technologies. This leads to the necessity of a precise, experimental feasible measure of entanglement. Nevertheless, such measurements are limited both from experimental uncertainties and intrinsic quantum bounds. Here we present an experiment where the amount of entanglement of a family of two-qubit mixed photon states is estimated with the ultimate precision allowed by quantum mechanics.

Figure 1

Experimental setup to generate polarization entangled photon pairs with variable entanglement and estimate its value with the ultimate precision allowed by quantum mechanics.

Figure 2

Estimation of entanglement at the quantum limit. The plot shows the estimated value of entanglement $⟨\widehat{ϵ}⟩$ as a function of the actual one ${ϵ}_t$. The uncertainty bars on $⟨\widehat{ϵ}⟩$ denote the quantity $\sqrt{\mathrm{Var}(\widehat{ϵ})\times ⟨K⟩}$, i.e., the square root of the sample variance multiplied by the average number of total coincidences $⟨K⟩$. The gray area corresponds to values within the inverse of the Fisher information ${ϵ}_t\pm H_{{ϵ}_t}^{-1/2}$. Uncertainty bars on the abscissae correspond to fluctuations $\delta {ϵ}_t=\sqrt{\mathrm{Var}(\widehat{p})}\sin 2\varphi$ in the determination of ${ϵ}_t$, due to fluctuations in the estimation of the mixing parameter.

Figure 3

Left: Fano factors of the coincidence counts $k_j$, $j=0$, 1, 2, 3. Each group contains the Fano factor for the seven values of $\varphi$ reported in the text. Right: estimated value of entanglement as a function of the actual one assuming, for the description of the output signals, the families ${\varrho }_{ϵ}$ (top plot) and ${\varrho }_{ϵ}^{\prime }$ (bottom plot). The uncertainty bars correspond to the $3\sigma$ confidence interval.