Efficient Decoherence-Free Entanglement Distribution over Lossy Quantum Channels

We propose and demonstrate a scheme for boosting the efficiency of entanglement distribution based on a decoherence-free subspace over lossy quantum channels. By using backward propagation of a coherent light, our scheme achieves an entanglement-sharing rate that is proportional to the transmittance $T$ of the quantum channel in spite of encoding qubits in multipartite systems for the decoherence-free subspace. We experimentally show that highly entangled states, which can violate the Clauser-Horne-Shimony-Holt inequality, are distributed at a rate proportional to $T$.

Figure 1

The concept of our DFS scheme. At step (a), Alice prepares a maximally entangled photon pair $A$ and $B$ and sends photon $B$ to Bob’s side. On the other hand, Bob sends an ancillary photon $R$ to Alice’s side. At step (b), Alice extracts the DFS by quantum parity checking on photons $A$ and $R$ and decodes back the initial entangled state from the DFS. For boosting the efficiency, we use a coherent light instead of a single photon $R$.

Figure 2

Our experimental setup.

Figure 3

The real parts of (a) ${\rho }_{AB}$ and (b) ${\rho }_{AB}^{\prime }$.

Figure 4

(a) The dependence of $F_{\mathrm{low}}$ on the transmittance $T$ in decibels. Dots with error bars are the derived values of $F_{\mathrm{low}}$ from $V_X$ and $V_Z$ in Table . The solid curve is obtained by theoretical calculation with $V_{\mathrm{sp}}\approx 0.90$ and experimental parameters. The broken line indicates the lower bound of the fidelity to a maximally entangled state to see the violation of the Clauser-Horne-Shimony-Holt inequality. (b) The experimental sharing rate of output states. The slope of the solid line fitted to the experimental data is $1.06\pm 0.04$, which clearly shows that the sharing rate is proportional to $T$. The broken line describes where an ideal single photon is used for mode $R$ instead of the coherent light pulse, whose rate is proportional to $T^2$. The two lines are expected to intersect at $T=\mu$.

Figure 5

The observed quantum interference by mixing photon $A$ in the state $|R{⟩}_A$ and the coherent light pulse $R$ with $D$ polarization, where $|R⟩\equiv |H⟩+i|V⟩$. The triangles and squares show the coincidence counts measured on the bases $|R{⟩}_E|D{⟩}_F$ and $|L{⟩}_E|D{⟩}_F$, respectively. Here $|L⟩\equiv |H⟩-i|V⟩$. The visibility at the zero delay is $0.83\pm 0.04$.