Experimental High-Dimensional Quantum Teleportation

Quantum teleportation provides a way to transmit unknown quantum states from one location to another. In the quantum world, multilevel systems which enable high-dimensional systems are more prevalent. Therefore, to completely rebuild the quantum states of a single particle remotely, one needs to teleport multilevel (high-dimensional) states. Here, we demonstrate the teleportation of high-dimensional states in a three-dimensional six-photon system. We exploit the spatial mode of a single photon as the high-dimensional system, use two auxiliary entangled photons to realize a deterministic three-dimensional Bell state measurement. The fidelity of teleportation process matrix is $F=0.596\pm 0.037$. Through this process matrix, we can prove that our teleportation is both nonclassical and genuine three dimensional. Our work paves the way to rebuild complex quantum systems remotely and to construct complex quantum networks.

Figure 1

Scheme for quantum teleportation of the high-dimensional states of a single photon. Alice wishes to teleport the high-dimensional quantum state of single photon 1 to Bob. Initially, Alice and Bob share a three-dimensional entangled photon pair 2–3. Then, Alice performs a high-dimensional Bell state measurement (HDBSM) assisted by another entangled photon pair 4–5 and sends the results to Bob through a classical channel. Finally, according to the results of HDBSM, Bob applies the appropriate three-dimensional Pauli operations on photon 3 to convert it into the original state of photon 1.

Figure 2

Experimental setup for teleporting a qutrit state of a single photon. A pulsed ultraviolet (UV) laser is focused on three sets of $\beta$-barium borate (BBO) crystals and produces three photon pairs in 2–3, $1-t$, and 4–5. The first pair, 2–3, is qutrit-qutrit entanglement in path DOF shared by Alice and Bob. The second pair, $1-t$, photon 1 is initialized in various states ($|{\phi }_1⟩-|{\phi }_{10}⟩$) to be teleported, triggered by its twisted photon $t$. The third pair, 4–5, is a polarization-entangled state, used as an ancillary pair for performing a HDBSM on photons 1 and 2.

Figure 3

Experimental results for quantum teleportation of three-dimensional single photon states $|{\phi }_1⟩-|{\phi }_{10}⟩$. We reconstruct the density matrix of the three-dimensional states by state tomography [38], and then obtain the fidelity of each state. Density matrix of the qutrits is reconstructed from a set of 9 measurements represented by operators $u_i$ (with $i=1$, $2,\dots 9$) and $u_i=|{\mathrm{\Psi }}_i⟩⟨{\mathrm{\Psi }}_i|$. Kets $|{\mathrm{\Psi }}_i⟩$ are selected from the following setting $|0⟩,|1⟩,|2⟩,(|0⟩+|1⟩)\sqrt{2},(|0⟩+i|1⟩)\sqrt{2},(|0⟩+|2⟩)\sqrt{2},(|0⟩+i|2⟩)\sqrt{2},(|1⟩+|2⟩)\sqrt{2},(|1⟩+i|2⟩)\sqrt{2}$. Average fidelity ($F=0.685\pm 0.027$) of 10 states is significantly higher than that of nonclassical quantum teleportation bound (0.5). Error bars are calculated from Poissonian counting statistics of the raw detection events.

Figure 4

Quantum process tomography of three-dimensional quantum teleportation. (a),(b), The real [$\mathrm{Re}({\chi }_{lk})$] and imaginary [$\mathrm{Im}({\chi }_{lk})$] values of the components of the reconstructed quantum process matrix, with l, $k=0$, 1, 2,..., 8. The results of the state tomography of the nine teleported states, $|{\phi }_1⟩-|{\phi }_9⟩$, are employed to reconstruct the process matrix of teleportation. The operator ${\sigma }_0-{\sigma }_8$ are Pauli matrices in three dimensions. For the ideal case, the only nonzero component of the process matrix of quantum teleportation, ${\chi }_{\text{ideal}}$, is $({\chi }_{\text{ideal}}{)}_{00}=1$, which is indicated by the transparent column.