Continuous-variable entanglement distillation between remote quantum nodes

The development of quantum network relies on high-quality entanglement between remote quantum nodes. In reality the unavoidable decoherence limits the quality of entangled quantum nodes, however, entanglement distillation can overcome this problem. Here we propose an experimentally feasible scheme of continuous-variable entanglement generation, storage, and distillation between distant quantum nodes, which only requires the atomic ensemble quantum memory and balanced homodyne detection (BHD). Initially one copy of a bipartite entangled state of light, suffering phase fluctuations during the distributions, is stored in two distant atomic ensembles so that the atomic ensembles are entangled. Within the storage lifetime, by distributing and storing another copy of entangled optical modes in these two atomic ensembles, the distillation on entangled atomic spin waves can be implemented based on the post-selection of the BHD result. Our scheme provides a highly entangled state between remote quantum nodes for downstream applications, and enables the extension to multipartite entanglement distillation in a large-scale quantum network.

Figure 1

Schematic of entanglement distillation between two distant atomic ensembles. (a) Generation and distribution of one copy of entangled optical modes to two remote atomic ensembles. $A_1^{0\left(1\right)}$ and $A_2^{0\left(1\right)}$ are atomic ensembles before (after) the first quantum storage. (b) Entanglement distillation by means of storing another copy of entangled optical modes in these two atomic ensembles, and BHD based post-selection. $A_1^2$ and $A_2^2$ are atomic ensembles after entanglement distillery. The insert is the structure of the optical chopper.

Figure 2

The dependence of total variance ${\mathrm{\Delta }}_A$ on the storage efficiency ${\eta }_S$. The dash-dot line is QNL. The solid line ${\mathrm{\Delta }}_A^{\mathrm{dis}}$ corresponds to the case with entanglement distillation, and the dashed line ${\mathrm{\Delta }}_A^{in}$ is for the case without entanglement distillation.

Figure 3

The total variance ${\mathrm{\Delta }}_A$ versus the phase noise. The dash-dot line is QNL. The solid (dashed) line corresponds to the case with (without) entanglement distillation.

Figure 4

(a) The function of total variance ${\mathrm{\Delta }}_A$ on the threshold $Q$ for different phase diffusion noise. Curves (1), (2), and (3) depict the total variances before distillation with phase diffusions $\sigma =0.7,\sigma =0.5$, and $\sigma =0.3$, respectively; curves (4), (5), and (6) depict the total variances after distillation with phase diffusions $\sigma =0.7,\sigma =0.5$, and $\sigma =0.3$, respectively; curve (7) shows QNL. (b) Distillation probability $P$ versus the threshold $Q$.