Quantum state transfer between two photons with polarization and orbital angular momentum via quantum teleportation technology

Quantum teleportation is a useful quantum information technology to transmit quantum states between different degrees of freedom. Here we report a quantum state transfer experiment in the linear optical system, transferring a single-photon state in the polarization degree of freedom (DoF) to another photon in the orbital angular momentum (OAM) quantum state via a biphoton OAM entangled channel. Our experimental method is based on quantum teleportation technology. The differences between ours and the original teleportation scheme is that the transfer state is known in ours, and our method is for different particles with different DoFs, while the original one is for different particles with the same DoF. In addition, our present experiment is implemented with a high Bell efficiency since each of the four hybrid-entangled Bell states can be discriminated. We use six states of poles of the Bloch sphere to test our experiment, and the fidelity of the quantum state transfer is $91.8\pm 1.3\%$.

Figure 1

Scheme of quantum state transfer. A polarization input state $c$ at Alice is transmitted to Bob using a shared OAM maximum entangled state $|{\varphi }_{-}{\rangle }_{ab}$ and a classical communication channel. Alice performs a hybrid-DoF Bell state measurement on her systems, $a$ and $c$, and communicates the outcome to Bob. Bob can check his qubit $b$ under the conditional outcome information from Alice.

Figure 2

Experimental setup, (a),(b) Measurement of OAM quantum states in antibunching and bunching, respectively. (c) Experimental setup for polarization-OAM quantum state transfer, in which the OAM entangled source is located in the pink box, any polarization quantum state of Alice's qubit $c$ can be prepared by the HWP and QWP located in the black box (Between Source and BSM Parts), and the hybrid-DoFs (OAM and polarization) Bell-state measurement is located in the green box. PPKTP: poled potassium titanyl phosphate; PBS: polarizing beam splitter; BS: beam splitter; HWP: half-wave plate; QWP: quarter-wave plate; SPP: spiral phase plate; M: mirror; SMF: single-mode fiber; SPAD: single-photon avalanche detector.

Figure 3

Two-photon OAM HOM interference results for Fig. 2 on different measurement bases, where $|D\rangle =\left(\right|+{\ell }_0\rangle +|-{\ell }_0\rangle )/\sqrt{2}$, $|A\rangle =\left(\right|+{\ell }_0\rangle -|-{\ell }_0\rangle )/\sqrt{2}$, $|R\rangle =\left(\right|+{\ell }_0\rangle +\mathrm{i}|-{\ell }_0\rangle )/\sqrt{2}$, and $|L\rangle =\left(\right|+{\ell }_0\rangle -\mathrm{i}|-{\ell }_0\rangle )/\sqrt{2}$. Since the fitting curves are close to each other and the error bars are small under the coordinate of this figure, error bars are not drawn, for a better presentation.

Figure 4

Tomography of the transmitted states. The input states prepared on qubit $c$ are the six poles of the Bloch sphere, $|0\rangle =|H\rangle$, $|1\rangle =|V\rangle$, $|D\rangle =\left(\right|H\rangle +|V\rangle )/\sqrt{2}$, $|A\rangle =\left(\right|H\rangle -|V\rangle )/\sqrt{2}$, $|R\rangle =\left(\right|H\rangle +\mathrm{i}|V\rangle )/\sqrt{2}$, and $|L\rangle =\left(\right|H\rangle -\mathrm{i}|V\rangle )/\sqrt{2}$, respectively. Colored bars show the experimental results.

Figure 5

Fidelities of teleported states. The fidelity is calculated according to $F=\langle \psi \left|\rho \right|\psi \rangle$, where $|\psi \rangle$ is one of the six mutually unbiased basis states. All fidelities are greater than the classical teleportation bound, $F_{\mathrm{class}}=2/3$.