Amending entanglement-breaking channels via intermediate unitary operations

We report a bulk optics experiment demonstrating the possibility of restoring the entanglement distribution through noisy quantum channels by inserting a suitable unitary operation (filter) in the middle of the transmission process. We focus on two relevant classes of single-qubit channels consisting in repeated applications of rotated phase-damping or rotated amplitude-damping maps, both modeling the combined Hamiltonian and dissipative dynamics of the polarization state of single photons. Our results show that interposing a unitary filter between two noisy channels can significantly improve entanglement transmission. This proof-of-principle demonstration could be generalized to many other physical scenarios where entanglement-breaking communication lines may be amended by unitary filters.

Figure 1

Scheme of the experimental setup. A source of polarization entangled qubits sends the $a$ photon directly to the tomography stage, while the $s$ photon is transmitted by a SMF to the simulation of $\mathrm{\Omega }=\mathrm{\Phi }\circ \mathrm{\Phi }$ or ${\mathrm{\Omega }}^{\prime }=\mathrm{\Phi }\circ \mathcal{F}\circ \mathrm{\Phi }$ and then measured in the same temporally synchronized bipartite tomography. The maps $\mathrm{\Phi }={\mathrm{\Phi }}_{\text{PD}}$ or $\mathrm{\Phi }={\mathrm{\Phi }}_{\text{AD}}$ are represented by the black boxes, while $\mathcal{F}={\mathrm{\Lambda }}_{\phi }$ is represented by the transparent-gray box enclosing a half-wave plate $\text{HWP}\left(\phi \right)$. Finally, we specify that $\mathrm{\Omega }$ (${\mathrm{\Omega }}^{\prime }$) corresponds to the absence (presence) of $\text{HWP}\left(\phi \right)$.

Figure 2

Single-channel modules. (a) Plot of ${\mathrm{\Phi }}_{\text{PD}}$: The unrotated yellow plate $\text{HWP}\left(0\right)$ constitutes the PD channel $\mathrm{\Gamma }$, since $\mathbb{I}$ is applied when it is absent or ${\sigma }_z$ when it is present. (b) Plot of ${\mathrm{\Phi }}_{\text{AD}}$: The SI and MZI constitute the AD channel $\mathrm{\Sigma }$, transforming the vertical polarization into horizontal by a rotation of $\text{HWP}\left(\alpha \right)$. In both (a) and (b), the rotating red plate $\text{HWP}\left(\theta \right)$ represents ${\mathrm{\Lambda }}_{\theta }$.

Figure 3

Concurrence vs PD mapping for $p=0.65$. Red points represent the experimental data. Blue lines represent the simulated data for perfect optical elements and a pure entangled state with $F=1$. Green shaded areas represent the regions of simulated data for realistic optical elements and a mixed entangled state within one standard deviation of the fidelity $F_{\text{exp}}=0.980\pm 0.016$. (a) Plot of ${\mathrm{\Omega }}_{\text{PD}}$, obtained by rotating $\theta$, with EB behavior around $\theta =\pm \frac{\pi }{8}$. (b) Plot of ${\mathrm{\Omega }}_{\text{PD}}^{\prime }$, obtained by rotating $\phi$, with a revival of entanglement around $\phi =\pm \frac{\pi }{8}$, while $\theta$ is fixed at $\frac{\pi }{8}$.

Figure 4

Concurrence vs AD mapping for $\eta =0.66$. Red points represent the experimental data. Blue lines represent the simulated data for perfect optical elements and a pure entangled state with $F=1$. Green shaded areas represent the regions of simulated data for realistic optical elements and a mixed entangled state within one standard deviation of the fidelity $F_{\text{expt}}=0.980\pm 0.016$ and the propagated error of the damping $\eta =0.66\pm 0.017$. (a) Plot of ${\mathrm{\Omega }}_{\text{AD}}$, obtained by rotating $\theta$, with EB behavior around $\theta =\pm \frac{\pi }{4}$. (b) Plot of ${\mathrm{\Omega }}_{\text{AD}}^{\prime }$, obtained by rotating $\phi$, with a revival of entanglement around $\phi =\pm \frac{\pi }{4}$, while $\theta$ is fixed at $\frac{\pi }{4}$.