Figure 1

Two schemes of the protocol for distribution of CV entanglement by separable Gaussian states. In the original scheme [4] (empty circle and ellipses) Alice’s mode $A$ and Bob’s distant mode $B$ are prepared in suitable rotated squeezed vacuum states while mode $C$ is hold by Alice and it is in a vacuum state. In the improved scheme of Sec. 4 (hatched circle and ellipses) modes $A$ and $C$ hold by Alice are in the momentum and position-squeezed vacuum states, respectively, and Bob’s mode $B$ is in a vacuum state. All the three modes are then displaced by displacements $D_A$, $D_B$, and $D_C$ distributed randomly with Gaussian distribution with covariance matrix $Q$ ($\tilde{Q}$ for the improved protocol) after which the modes are in a fully separable state (step 1). Mixing of modes $A$ and $C$ on a balanced beam splitter $B{S}_{AC}$ entangles mode $A$ with the pair of modes $\left(BC\right)$ while mode $B$ is separable from $\left(AC\right)$ and mode $C$ is separable from $\left(AB\right)$ (step 2). Mixing of modes $B$ and $C$ on a balanced beam splitter $B{S}_{BC}$ finally entangles $A$ and $B$ while $C$ still remains separable from $\left(AB\right)$ (step 3). See text for details.Reuse & Permissions

Figure 2

Scheme of the protocol for recovery of the entanglement between modes $A$ and $C$. Mode $A$ in a suitable momentum-squeezed vacuum state and mode $C$ in a position-squeezed vacuum state with the same level of squeezing are displaced by displacements $D_A$ and $D_C$ distributed randomly with Gaussian distribution characterized by the covariance matrix $\tilde{Q}$ (16). Next, the two modes are mixed on a balanced beam splitter $B{S}_{AC}$ that prepares them in a two-mode separable state. Classical information traveling to Bob is then used for displacement $D_B^{\left(G\right)}$ of mode $C$ with a suitable electronic gain $G$. Provided that the gain is adjusted appropriately, the entanglement between modes $A$ and $C$ can be perfectly recovered. See text for details.Reuse & Permissions