Experimental Entanglement Redistribution under Decoherence Channels

When an initially entangled pair of qubits undergoes local decoherence processes, there are a number of ways in which the original entanglement can spread throughout the multipartite system consisting of the two qubits and their environments. Here, we report theoretical and experimental results regarding the dynamics of the distribution of entanglement in this system. The experiment employs an all optical setup in which the qubits are encoded in the polarization degrees of freedom of two photons, and each local decoherence channel is implemented with an interferometer that couples the polarization to the path of each photon, which acts as an environment. We monitor the dynamics and distribution of entanglement and observe the transition from bipartite to multipartite entanglement and back, and show how these transitions are intimately related to the sudden death and sudden birth of entanglement. The multipartite entanglement is further analyzed in terms of three- and four-partite entanglement contributions, and genuine four-qubit entanglement is observed at some points of the evolution.

Figure 1

Experimental setup: An ultraviolet laser pumps a nonlinear BBO crystal, and two photons are produced via parametric down-conversion. Both photons are directed to separated nested interferometers. The first interferometers (light red rectangles) have a BD and a MBD. These implement the decoherence channels, as in Refs. [8, 9]. The optical elements in the light green rectangles serve to perform tomographic measurements on the polarization and path degrees of freedom simultaneously.

Figure 2

Experimental entanglements versus $p$, the evolution parameter. $C_{S_1{S}_2}^2$ is plotted in red squares and $C_{E_1{E}_2}^2$ in blue circles. Black diamonds represent the residual entanglement of Eq. (6), in the lower-bound approximation. The areas are theoretical predictions (see the text). The inset shows the evolution of $\mathrm{\Gamma }$ [see Eq. (2)].

Figure 3

Three-tangles ${\tau }_{\underset{\_}{i}jk}$ in the quasipure approximation versus $p$. Red circles represent ${\tau }_{\underset{\_}{S_1}{S}_2{E}_2}$, black diamonds ${\tau }_{\underset{\_}{S_2}{S}_1{E}_1}$, blue squares ${\tau }_{\underset{\_}{E_1}{S}_2{E}_2}$, and magenta stars ${\tau }_{\underset{\_}{E_2}{S}_1{E}_1}$. The dashed lines are a theoretical prediction for pure states.

Figure 4

Fidelity with respect to the Dicke state $|\mathcal{D}⟩$ versus $p$. The line is the theoretical evolution of the experimental initial state.