Teleportation of two-mode squeezed states

We consider two-mode squeezed states which are parametrized by the squeezing parameter and the phase. We present a scheme for teleporting such entangled states of continuous variables from Alice to Bob. Our protocol is operationalized through the creation of a four-mode entangled state shared by Alice and Bob using linear amplifiers and beam splitters. Teleportation of the entangled state proceeds with local operations and the classical communication of four bits. We compute the fidelity of teleportation and find that it exhibits a trade-off with the magnitude of entanglement of the resultant teleported state.

Figure 1

Schematic diagram for the teleportation protocol. Alice’s amplifier SA3 generates the two-mode entangled state $\left(x_7,x_8\right)$ to be teleported. Bob has two amplifiers TA1 and TA2 and two beam splitters BS1 and BS2 with which he generates a four-mode state $\left(x_5,x_6,x_{15},x_{16}\right)$. He keeps two of these modes $x_5$ and $x_{16}$ with himself and sends the remaining two modes $x_6$ and $x_{15}$ to Alice. Using the beam splitters BS3 and BS4 Alice combines her modes $x_7$ and $x_8$ with those sent by Bob, and performs four measurements on the output modes $x_9,x_{10},x_{11},x_{12}$. She then communicates her results to Bob who uses these to apply a unitary transformation to displace the modes $x_5$ and $x_{16}$. The final teleported state is found in the modes $x_{13}$ and $x_{14}$.

Figure 2

(Color online) The logarithmic negativity $E_n$ for the final teleported state is plotted versus the squeezing $q$ of the two-mode state generated from the source amplifier SA3 ($x$ axis) and the squeezing $r$ of the two two-mode states from the teleportation amplifiers TA1 and TA2, respectively ($y$ axis).

Figure 3

(Color online) The fidelity of teleportation $F$ is plotted versus the squeezing $q$ of the state to be teleported ($x$ axis) and the squeezing $r$ of the output modes of the amplifiers TA1 and TA2 ($y$ axis).