Quantum teleportation of multiple degrees of freedom of a single photon

Abstract

Quantum teleportation1 provides a ‘disembodied’ way to transfer quantum states from one object to another at a distant location, assisted by previously shared entangled states and a classical communication channel. As well as being of fundamental interest, teleportation has been recognized as an important element in long-distance quantum communication2, distributed quantum networks3 and measurement-based quantum computation4,5. There have been numerous demonstrations of teleportation in different physical systems such as photons6,7,8, atoms9, ions10,11, electrons12 and superconducting circuits13. All the previous experiments were limited to the teleportation of one degree of freedom only. However, a single quantum particle can naturally possess various degrees of freedom—internal and external—and with coherent coupling among them. A fundamental open challenge is to teleport multiple degrees of freedom simultaneously, which is necessary to describe a quantum particle fully and, therefore, to teleport it intact. Here we demonstrate quantum teleportation of the composite quantum states of a single photon encoded in both spin and orbital angular momentum. We use photon pairs entangled in both degrees of freedom (that is, hyper-entangled) as the quantum channel for teleportation, and develop a method to project and discriminate hyper-entangled Bell states by exploiting probabilistic quantum non-demolition measurement, which can be extended to more degrees of freedom. We verify the teleportation for both spin–orbit product states and hybrid entangled states, and achieve a teleportation fidelity ranging from 0.57 to 0.68, above the classical limit. Our work is a step towards the teleportation of more complex quantum systems, and demonstrates an increase in our technical control of scalable quantum technologies.

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Figure 1: Scheme for quantum teleportation of the spin–orbit composite states of a single photon.
Figure 2: Experimental set-up for teleporting multiple properties of a single photon.
Figure 3: Experimental results for quantum teleportation of spin–orbit product states , , and of a single photon.
Figure 4: Experimental results for quantum teleportation of spin–orbit entanglement of a single photon.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China, the Chinese Academy of Sciences and the National Fundamental Research Program (grant no. 2011CB921300).

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Authors

Contributions

C.-Y.L. and J.-W.P. had the idea for and designed the research; X.-L.W., X.-D.C., Z.-E.S., M.-C.C., D.W., L.L., N.-L.L. and C.-Y.L. performed the experiment; X.-L.W., M.-C.C., C.-Y.L. and J.-W.P. analysed the data; C.-Y.L. and J.-W.P. wrote the paper with input from all authors; and N.-L.L., C.-Y.L. and J.-W.P. supervised the whole project.

Corresponding authors

Correspondence to Chao-Yang Lu or Jian-Wei Pan.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Hong–Ou–Mandel interference of multiple independent photons encoded with SAM or OAM.

a, Interference at the PBS where input photons 1 and 2 are intentionally prepared in the states (orthogonal SAMs; open squares) and (parallel SAMs; solid circles). The y axis shows the raw fourfold (the trigger photon t and photons 1, 2 and 3) coincidence counts. The extracted visibility is 0.75 ± 0.03, calculated from V(0) = (C+ − C//)/(C+ + C//), where C// and C+ are the coincidence counts without any background subtraction at zero delay for parallel and, respectively, orthogonal SAMs. The red and blue lines are Gaussian fits to the raw data. b, Two-photon interference on beam splitter 1, where photons 1 and 4 are prepared in orthogonal OAM states. The black line is a Gaussian fit to the raw data of fourfold (the trigger photon and photons 1, 4 and 5) coincidence counts. The visibility is 0.73 ± 0.03, calculated from V(0) = 1 – C0/C, where C0 and C is the fitted counts at zero and, respectively, infinite delays. c, Two-photon interference at beam splitter 2, where input photons 1 and 5 are prepared in the orthogonal OAM states. The black line is a Gaussian fit to the data points. The interference visibility is 0.69 ± 0.03 calculated in the same way as in b. Error bars, 1 s.d., calculated from Poissonian counting statistics of the raw detection events.

Extended Data Figure 2 A universal scheme for teleporting N DoFs of a single photons.

a, A scheme for teleporting two DoFs of a single photon using three beam splitters, which is slightly different from the one presented in the main text using a PBS and two beam splitters. Through the first beam splitter, six asymmetric states, and , can result in one photon in each output, which is ensured by teleportation-based QND on the Y DoF. After passing the two photons through the two filters that project them into the and states for the X DoF, four states, and , survive. Through the second beam splitter, only the asymmetric state of the Y DoF can result in one photon in each output. Finally we can discriminate the state from the 16 hyper-entangled Bell states. b, Teleportation of three DoFs of a single photons (Methods). Note that to ensure that there is one and only one photon in the output of the first beam splitter, we can use the teleportation-based QND on two DoFs in a (dashed circle). c, Generalized teleportation of N DoFs of a single photons. The h-BSM on N DoFs can be implemented as follows: (1) the beam splitter post-selects the asymmetric hyper-entangled Bell states in N DoFs which contain an odd number of asymmetric Bell states in one DoF, (2) two filters and one bit-flip operation erase the information on the measured DoF and further post-select asymmetric states, and (3) teleportation-based QND.

Extended Data Figure 3 Active feed-forward for spin–orbit composite states.

a, The active feed-forward scheme. This composite active feed-forward could be completed in a step-by-step manner. First, we use an EOM to implement the active feed-forward for SAM qubits. It is important to note that EOM does not affect OAM. Second, we use a coherent quantum SWAP gate between the OAM and SAM qubits. The original OAM is converted into a ‘new’ SAM, whose active feed-forward operation is done by a second EOM. Then the OAM and SAM qubits undergo a second SWAP operation and are converted to the original DoFs. b, The quantum circuit for a SWAP gate between the OAM and SAM qubits. The SWAP gate is composed of three CNOT gates: in the first and third CNOT gates, the SAM and OAM qubits act as the control and target qubits, respectively, whereas in the second CNOT gate this is reversed.

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Wang, X., Cai, X., Su, Z. et al. Quantum teleportation of multiple degrees of freedom of a single photon. Nature 518, 516–519 (2015). https://doi.org/10.1038/nature14246

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