Figure 1

Two schemes for entanglement purification using polarizing beam splitters. (a) The scheme that was proposed in Ref. 3. $S_1$ and $S_2$ are two ideal sources of polarization entangled photon pairs, each of which emits exactly one pair. If exactly one photon is detected in modes $a_2$ and $b_2$ behind the PBS, then the remaining pair of photons in modes $a_1$ and $b_1$ is purified. (b) The new scheme that uses two parametric down-conversion sources, such that the probabilities to produce two photons each into modes $a_1$ and $b_1$ and none into modes $a_2$ and $b_2$ or vice versa are comparable to the probability of producing one photon into each mode. It is essential for the scheme that one can fix the relative phases between these different possibilities, leading to spatial entanglement in addition to the polarization entanglement. Under this condition, if there is one photon in each output mode behind the PBS, then both the pair of photons in modes $a_1$ and $b_1$ and the pair in modes $a_2$ and $b_2$ have purified polarization entanglement.Reuse & Permissions

Figure 2

This plot shows the polarization entanglement fidelity after purification as a function of the fidelity before purification for different schemes and parameter values. The three full-line curves show the performance of our scheme, where the top one is for perfect spatial entanglement, i.e., $r=\cos \varphi =1$, and the two others are for $r=\cos \varphi =0.95$ and $r=\cos \varphi =0.9$. The dashed S-shaped curve shows the performance of the protocols of Refs. 1, 3 under ideal conditions. The straight line corresponds to equal input and output fidelities. It is important to note that the new scheme produces two entangled pairs instead of one. One sees that the new protocol does not have a lower threshold fidelity, while the upper threshold is determined by the quality of the spatial entanglement.Reuse & Permissions