Avoiding disentanglement of multipartite entangled optical beams with a correlated noisy channel

Abstract

A quantum communication network can be constructed by distributing a multipartite entangled state to space-separated nodes. Entangled optical beams with highest flying speed and measurable brightness can be used as carriers to convey information in quantum communication networks. Losses and noises existing in real communication channels will reduce or even totally destroy entanglement. The phenomenon of disentanglement will result in the complete failure of quantum communication. Here, we present the experimental demonstrations on the disentanglement and the entanglement revival of tripartite entangled optical beams used in a quantum network. We experimentally demonstrate that symmetric tripartite entangled optical beams are robust in pure lossy but noiseless channels. In a noisy channel, the excess noise will lead to the disentanglement and the destroyed entanglement can be revived by the use of a correlated noisy channel (non-Markovian environment). The presented results provide useful technical references for establishing quantum networks.

Figure 1. Schematic of principle and experimental set-up.

(a) Two modes ( and ) of a tripartite entangled state are distributed over two lossy quantum channels to Alice and Claire, respectively. (b) One mode of the tripartite entangled state is distributed over a noisy channel, where disentanglement is observed among optical modes and . The entanglement revival operation is implemented by coupling an ancillary beam () who has correlated noise with the environment with the transmitted mode on a beam-splitter with transmission efficiency of , thus the entanglement among modes , and is revived. (c) The schematic of experimental set-up for distributing a mode of the tripartite entangled optical beams over a noisy channel and the entanglement revival. T1 and T2 are the beam-splitters used to generate the GHZ entangled state. η_A and T are the transmission efficiencies of the noisy channel and the revival beam-splitter, respectively. HD1-3, homodyne detectors. LO, the local oscillator.

Figure 2. The entanglement in lossy channels.

(a) One optical mode is distributed in the lossy channel (η_A ≠ 1, η_C = 1). (b) Two optical modes and are distributed in the lossy channels with the same transmission efficiency (η_A ≠ 1, η_C ≠ 1). PPT values are all below the entanglement boundary (red lines), which means that the tripartite entanglement is robust against loss in quantum channels. The black, blue and pink dots represent the experimental data for different PPT values, respectively. Error bars represent ± one standard deviation and are obtained based on the statistics of the measured noise variances.

Figure 3. The entanglement properties of different asymmetric tripartite states in two lossy channels.

(a,b) PPT values of fully robust entanglement against loss with c_x/c = 0.8. (c,d) PPT values of a one-mode fragile state in lossy channels for attenuations with c_x/c = 0.5. (e,f) A totally one-mode biseparable state in lossy channels with c_x/c = 0.3.

Figure 4. The disentanglement and entanglement revival in a noisy channel.

(a) The PPT values for the transmission in a noisy channel, where the variance of the excess noise is taken as five times of shot noise level. The tripartite entangled state experiences entanglement (I), one-mode biseparable (II) and fully disentanglement (III) along with the decreasing of the channel efficiency. (b) The PPT values after entanglement revival. Dash lines are the corresponding results of the perfectly revival, the results are the same with the lines in Fig. 2(a) which are obtained before disentanglement. The black dots represent the experimental data. Error bars represent ± one standard deviation and are obtained based on the statistics of the measured noise variances.

Figure 5. The disentanglement and revival of entanglement at different noise levels (in the unit of shot noise level).

(a) Disentanglement at different excess noise levels. (b) The PPT values after entanglement revival, and it is independent on the excess noise. The black dots represent the experimental data. Error bars represent ± one standard deviation and are obtained based on the statistics of the measured noise variances.