Experimental Entanglement Distribution by Separable States

Distribution of entanglement between macroscopically separated parties is crucial for future quantum information networks. Surprisingly, it has been theoretically shown that two distant systems can be entangled by sending a third system that is not entangled with either of them. Here, we experimentally distribute entanglement and successfully prove that our transmitted light beam is indeed not entangled with the parties’ local systems. Our work demonstrates an unexpected variant of entanglement distribution and improves the understanding necessary to engineer multipartite quantum networks.

Figure 1

Principle of entanglement distribution by separable states. In the beginning, Alice possesses two separable modes $A$ and $C$. Both modes are also separable with respect to Bob’s mode $B$. Alice sends mode $C$ to Bob, and he combines his mode $B$ with the received mode $C$. Finally, Alice and Bob share an entangled system $A|B^{\prime }$, which can be traced back to the initial entanglement for the $A|BC$ splitting.

Figure 2

Experimental setup for entanglement distribution by separable states. The three-mode state is prepared by overlapping a squeezed state, a vacuum state, and a thermal state at two balanced beam splitters. This step is analogous to the interference of modes $A$ and $C$ in the original protocol [7], and the state preparation procedure does not create any entanglement between mode $B$ and modes $A$ and $C$. After modes $A$ and $C$ have been sent to Alice and mode $B$ has been sent to Bob, the $B|AC$ and $C|AB$ separability is carefully checked with balanced homodyne detectors ${\mathrm{BHD}}_A$, ${\mathrm{BHD}}_B$, and ${\mathrm{BHD}}_C$. Subsequently, Alice sends separable mode $C$ to Bob. By overlapping modes $C$ and $B$ at another balanced beam splitter ${\mathrm{BS}}_3$, entanglement is established between Alice and Bob, which is verified by balanced homodyne detectors ${\mathrm{BHD}}_A$ and ${\mathrm{BHD}}_{B^{\prime }}$. For details on the squeezed-light source and the generation of the thermal state, see the Supplemental Material [20].

Figure 3

Separability analysis. Theoretical simulations of the ${\mathrm{PPT}}_C$ value with respect to the added thermal noise (given in dB above vacuum noise variance) are depicted. The solid lines correspond to 10 dB initial squeezing with different losses. To obtain the required PPT value ($>1$), a minimal loss of 33% is necessary. The point of intersection with the threshold of 1 is exclusively depending on the loss and not on the actual initial squeezing value. The parameters, which were used in our measurements, are marked with the magenta cross.

Figure 4

Measured PPT values with subtraction of detection losses. The magenta curves show the inferred ${\mathrm{PPT}}_B$ and ${\mathrm{PPT}}_C$ values of the measured covariance matrix $\gamma$ for a spectrum of computationally eliminated detection losses. Based on independent measurements, we estimate the actual detection loss to be greater 7% and smaller 22%. These losses do not push the PPT values below unity. The successful demonstration of our protocol is thus independent of the question of whether detection loss should be corrected for or not.