Abstract
Quantum teleportation can transfer an unknown quantum state between distant quantum nodes, which holds great promise in enabling largescale quantum networks. To advance the full potential of quantum teleportation, quantum states must be faithfully transferred at a high rate over long distance. Despite recent impressive advances, a highrate quantum teleportation system across metropolitan fiber networks is extremely desired. Here, we demonstrate a quantum teleportation system which transfers quantum states carried by independent photons at a rate of 7.1 ± 0.4 Hz over 64kmlong fiber channel. An average singlephoton fidelity of ≥90.6 ± 2.6% is achieved, which exceeds the maximum fidelity of 2/3 in classical regime. Our result marks an important milestone towards quantum networks and opens the door to exploring quantum entanglement based informatic applications for the future quantum internet.
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Introduction
Quantum teleportation^{1} enables the ‘disembodied’ transfer of an unknown quantum state to a remote location by using quantum entanglement resource with the help of quantum measurement and classical communication. It lies at the heart of the realization of quantum information technologies such as quantum network^{2,3,4} and distributed quantum computation^{5}. Since its initial proposal by Bennett et al. in 1993^{1}, quantum teleportation has been demonstrated in various platforms, including atomic ensembles^{6}, single atoms^{7}, trapped ions^{8,9}, solidstate quantum systems^{10}, nuclear magnetic resonance^{11} and quantum optics^{12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33}. Teleportation systems based on quantum optics offer a promising avenue towards quantum networks, which can be realized in continuousvariable (CV) and discretevariable (DV) systems, respectively. For instance, the transfer and retrieval for both coherent states^{28,29,30,31} and nonclassical states^{32} have been experimentally realized with optical modes in CV systems, providing a method to realize deterministic quantum teleportation. However the distance of CV system is limited to around ten kilometers^{30,31}, due to the possible increased fragility with respect to the losses of quantum channels^{34}. For globalscale quantum networks^{2,3}, the distribution range of quantum states needs to be greatly extended to thousands of kilometers using quantum teleportation in DV systems. Till now, this has been realized with multiple degrees of freedom over several meters to more than one thousand kilometers, from the tabletop experiments^{12,13,14,15,16,17} to realworld demonstrations^{18,19,20,21,22,23,24,25,26}. Especially, by using a lowEarth orbit Micius satellite^{35}, quantum teleportation over 1200 km has been achieved^{25,26}. Despite impressive results, a highrate quantum teleportation system has yet to be demonstrated, which is desired for advancing the development of quantum networks.
Here we report an experimental realization of a Hertzrate quantum teleportation system through fiber over a metropolitan range. Our demonstration relies on a highperformance timebin entangled quantum light source with a single piece of fiberpigtailed periodically poled lithium niobate (PPLN) waveguide. The quantum states to be teleported are carried by a weak coherent singlephoton source with decoy states. The indistinguishability of photons after prior quantum states distribution through fiber channels is ensured with a fully running feedback system. As an important feature of our demonstration, photonic timebin qubits are teleported at a rate of 7.1 ± 0.4 Hz over a 64kmlong fiber channel. An average singlephoton fidelity of ≥90.6 ± 2.6% is achieved with the decoy state method. Our implementation establishes an important milestone towards quantum internet.
Results
Experimental setup
Figure 1a shows an aerial photography of the campus of University of Electronic Science and Technology of China (UESTC) indicating the distances between the locations Alice, Bob and Charlie. Figure 1b shows the scheme of our teleportation system, and Fig. 2 depicts its experimental setup. To be compatible with the structure of quantum networks^{36}, the quantum state to be teleported should be carried by an independent singlephoton source, which is different with the Rome scheme^{13}. In our demonstration, the quantum bit (qubit) sender, Alice, located at a switching room of the backbone network on the campus, prepares a weak coherent singlephoton source, which is used to encode photonic timebin qubit, i.e., a singlephoton wavepacket in a coherent superposition of two time bins. The timebin qubit is obtained by passing the singlephoton wavepacket through an unbalanced Mach–Zehnder interferometer (UMZI) with pathlength difference ∆τ. The timebin qubit can be written as \({\psi {{\rangle }}}_{{\rm{A}}}=\alpha {e}{{\rangle }}+\beta {e}^{i\phi }{l}{{\rangle }}\), where \({e}{{\rangle }}\) represents the early time bin (i.e., a photon having passed through the short arm of the interferometer); \({l}{{\rangle }}\) is the late time bin (i.e., a photon having passed through the long arm); ϕ is a relative phase between \({e}{{\rangle }}\) and \({l}{{\rangle }}\), and \({\alpha }^{2}+{\beta }^{2}=1\). Alice sends the created quantum states carried by singlephoton wavepackets to Charlie, located at a laboratory at a flight distance of 400 m away, through a quantum channel (QC) of 22 km, i.e., \(\text{Q}{\text{C}}_{\text{A}\to \text{C}}\), including 2 km deployed fiber in field and 20 km fiber spool. The quantum information receiver, Bob, located at another laboratory, 210 m from Charlie, shares with Charlie a pair of timebin entangled photonic qubits in the state of \({\varPhi }^{+}{{\rangle }}={2}^{1/2}({ee}{{\rangle }}+{ll}{{\rangle }})\), with one at 1549.16 nm (idler) and the other at 1531.87 nm (signal). The idler photons are distributed through another 22 km QC to Charlie, i.e., \(\text{Q}{\text{C}}_{\text{B}\to \text{C}}\), including 2 km deployed fiber in field and 20 km fiber spool. Charlie performs the joint Bellstate measurement (BSM) between the qubits sent by Alice and Bob, using a 50:50 fiber beam splitter (BS). We select only projections onto the singlet state of \({\psi }^{}{{\rangle }}={2}^{1/2}({el}{{\rangle }}{le}{{\rangle }})\), which can be realized by the detection of one photon in each output port of BS with a time difference of 625 ps. When a \({\psi }^{}{{\rangle }}\) has been successfully detected, the BSM result is sent to Bob over a classical channel (CC) by means of an optical pulse. In this case, the signal photons at Bob (stored in a 20kmlong fiber spool) are projected onto the state of \({\psi {{\rangle }}}_{{\rm{B}}}={\sigma }_{y}{\psi {{\rangle }}}_{{\rm{A}}}\), with σ_{y} being a Pauli matrix. The synchronization of the teleportation system is made through the CCs (see Materials and Methods). All fiber spools used in our system are nonzero dispersionshifted singlemode optical fiber (G.655, Yangtze Optical Fibre and Cable).
Prior entanglement distribution
The property of prior entanglement distribution is measured before performing the BSM of quantum teleportation. In the experiment, we distribute the idler photons through \(\text{Q}{\text{C}}_{\text{B}\to \text{C}}\) to Charlie while the signal photons are held by a 20 km spool of fiber at Bob. The distributed timebin entanglement property is characterized with the Franson interferometer, with details shown in Supplementary Note S1. The visibilities of twophoton interference fringes are 94.3 ± 0.1% and 93.5 ± 0.1%, respectively, as shown in Fig. 3a. The error bars of visibilities are calculated by Monte Carlo simulation assuming Poissonian detection statistics. This result indicates that the quantum entanglement property still maintains after being distributed over 42 km fiber channels. Furthermore, it also allows us to ensure that parameters of two UMZIs can be remotely set as the same in our setup, which is a crucial requirement for the quantum teleportation processes.
Indistinguishability of photons at Charlie
Alice’s and Bob’s photons need to be indistinguishable at Charlie for a successful BSM, which is difficult in long distance quantum teleportation. The spatial and spectral indistinguishabilities are ensured by using singlemode fibers and identical fiber Bragg grating (FBG) filters for both photons. The pathlength difference and polarization of the photons are stabilized with an active and automatic feedback system (see Materials and Methods). The experimental results of indistinguishabilities at Charlie are shown in Fig. 3b, c. With our fully running feedback system, we measure the HongOuMandel (HOM) interference curve^{37} with the timebin qubits from Alice and Bob, respectively. The result given in Fig. 3d shows a HOMdip with a visibility of 35.3 ± 1.0% by Gaussian fitting, approaching the upper bound of 40% between the coherent state and the thermal state, which corresponds to a singlephoton indistinguishability of 88.8 ± 2.4% at Charlie, with details shown in Supplementary Note S2.
Quantum teleportation results
Two classes of quantum states are prepared to be teleported from Alice to Bob: one class contains qubits lying on the equator of the Poincare sphere (coherent superpositions of \({e}{{\rangle }}\) and \({l}{{\rangle }}\) with equal amplitudes, \({\psi {{\rangle }}}_{{\rm{A}}}={2}^{1/2}({e}{{\rangle }}+{e}^{i\phi }{l}{{\rangle }})\), and the other class contains the two poles of the Poincare sphere (\({e}{{\rangle }}\) and \({l}{{\rangle }}\)). For the equatorial states, a successful teleportation implies Bob’s photon to be in a superposition state (\({\psi {{\rangle }}}_{{\rm{B}}}={\sigma }_{y}{\psi {{\rangle }}}_{{\rm{A}}}\)). Conditional on the successful BSM result from Charlie through CC, we observe sinusoidal curves of threefold coincidence with visibilities of 61.4 ± 4.0% and 60.0 ± 3.9% for two outputs of UMZI2, respectively, as shown in Fig. 3e. The maximum value of threefold coincidence counts is 335 ± 18 for 200 s, indicating that a quantum teleportation rate of 7.1 ± 0.4 Hz is achieved excluding an extra measurement loss of 6.25 dB, i.e., 5.30 dB from UMZI2 and 0.95 dB from singlephoton detection. With the measured visibilities, the fidelity for the equatorial states can be calculated as \({F}_{\text{equator}}=\left(1+V\right)/2\), corresponding to a fidelity of 80.4 ± 2.0% for the equatorial states^{15}, which alone can already represent a strong indication of the quantum teleportation. It is worth mentioning that all the visibilities are obtained without subtracting the background noise. With the UMZI1 in Alice removed, we directly prepare \({e}{{\rangle }}\) (\({l}{{\rangle }}\)) state with a single temporal mode and send it to Charlie for BSM. For the measurement, Bob removes the UMZI2 and accumulates threefold coincidence counts at the corresponding time bins within a coincidence window of 200 ps. The fidelity \({F}_{e/l}\) can be calculated by \({F}_{e/l}={R}_{\text{c}}/\left({R}_{\text{c}}+{R}_{\text{w}}\right)\), where R_{c} and R_{w} represent the probability of detecting the correct and wrong state in the pole basis, respectively. The measured fidelity for the \({e}{{\rangle }}\) input state is 92.2 ± 1.0% and for the \({l}{{\rangle }}\) input state 92.4 ± 1.1%. Assuming that the performance of equatorial states is the same, i.e., \({F}_{+}={F}_{}={F}_{+i}={F}_{i}={F}_{\text{equator}}\), we apply \({F}_{\text{avg}}=\left(4{F}_{\text{equator}}+{F}_{e}+{F}_{l}\right)/6\) to obtain an average fidelity of 84.3 ± 1.7%, which is significantly above the maximum fidelity of 2/3 in classical regime.
Furthermore, we reconstruct the density matrices ρ of the quantum states after teleportation using quantum state tomography (QST) method^{38}, as described in Supplementary Note S3. Four welldefined states (\({e}{{\rangle }}\), \({l}{{\rangle }}\), \(+\rangle\) and \(+i\rangle\), \(+{{\rangle }}={2}^{1/2}({e}{{\rangle }}+{l}{{\rangle }})\) and \(+i{{\rangle }}={2}^{1/2}({e}{{\rangle }}+{il}{{\rangle }})\) are created to perform QST in our system. We calculate fidelities of the quantum teleportation by \(F={ }_{\mathrm{B}}\langle\psi\rho \psi\rangle_{\mathrm{B}}\) with the expected states (\({\psi {{\rangle }}}_{{\rm{B}}}\)). Figure 4 shows the density matrices of four quantum states after teleportation obtained by QST. The fidelities for all four prepared states are given in Fig. 5, which exceed the maximum classical value of 2/3. The more decoherence of \(+{{\rangle }}\) and \(+i{{\rangle }}\) state results from the residual distinguishability of the photons (see Supplementary Note S2), which will not cause any effect on \({e}{{\rangle }}\) and \({l}{{\rangle }}\) states. This can be improved by further eliminating the distinguishability of photons in all degrees of freedom, i.e., spatial, spectral, temporal, and polarization degrees^{39}. The uncertainty of teleportation fidelities is calculated assuming Poissonian detection statistics and using Monte Carlo simulation. The average fidelity \({F}_{\text{avg}}=\left(2\left({F}_{+}+{F}_{+i}\right)+{F}_{e}+{F}_{l}\right)/6\) is 86.4 ± 4.5%, showing the quantum nature of the disembodied state transfer from Alice to Bob.
It is noted that the classical fidelity bound of 2/3 is only applied when Alice’s initial states carried with genuine single photons, rather than weak coherent states prepared with attenuated laser pulses. Here we utilize the decoy state method (DSM)^{40,41,42} to estimate the performance of our system given that genuine single photons are used^{24}. In the experiment, we prepare quantum states\({e}{{\rangle }}\), \({l}{{\rangle }}\), \(+\rangle\) and \(+i{{\rangle }}\) with varying the mean photon number per qubit at Alice among three values (\({\mu }_{\text{A}}^{\text{s}}=0.088\), \({\mu }_{\text{A}}^{\text{d}}=0.029\) and \({\mu }_{\text{A}}^{\text{v}}=0\), where \({\mu }_{\text{A}}^{\text{s}}\), \({\mu }_{\text{A}}^{\text{d}}\) and \({\mu }_{\text{A}}^{\text{v}}\) are the mean photon numbers of the signal, decoy and vacuum state, respectively) and perform quantum teleportation, with details shown in Supplementary Tables S3 and S4. Based on these results, we calculate the lower bounds of \({F}_{e/l}^{1}\) and \({F}_{+/+i}^{1}\) as shown in Fig. 5, with \({F}_{\text{avg}}^{1}\) ≥ 90.6 ± 2.6%, which significantly violates the classical bound of 2/3 by more than 9 standard deviations, clearly demonstrating the capability of our system for highfidelity teleportation. We present an analytical model of our teleportation system^{24}, and observe a good quantitative agreement between theory and experiment (see Supplementary Notes S4 and S5). Finally, we conclude the key metrics of our teleportation system in Table 1, where the stateoftheart teleportation systems in DV with photonic qubits sent by an independent source are summarized as a comparison. Note that, in Table 1, the statetransfer distance corresponds to the total length of quantum channel between Alice and Bob, while the teleportation distance is defined as the beeline spatial separation between the location of the BSM station and the signal photon at the time of the BSM projection^{24}.
Discussion
Metrics for a quantum network are of course the rate, fidelity and distance of quantum teleportation. Although our work has moved one important step closer to highspeed quantum teleportation over a metropolitan area, further increases of teleportation rate in our system could be reached by increasing the repetition rate of system, the efficiencies of SNSPDs and BSM, and using multiple spectral channels^{43}. Further insights into photonic quantum information encoding, the use of multiple degrees of freedom^{44} or multiple qubits^{45} will also certainly increase the information capacity of quantum teleportation system based on hyperentanglement Bellstate analysis^{46,47}. The deviations of the fidelity from unity in our system are mostly due to multiphoton events of quantum light sources and the remaining distinguishability of the two photons undergoing the BSM. We may replace the SNSPDs with photonnumber resolving SNSPDs^{48,49} to allow postselection of multiphoton events. Alternatively, another promising solution to multiphoton events from Alice is applying single quantum emitters that can generate individual photons deterministically^{50}. Further, the indistinguishability between the photons from Alice and Bob could be improved by using narrower FBGs (see Supplementary Note S2). To extend the teleportation distance, the combination of lowEarthorbit satellite links^{25,26} and quantum repeater architecture^{51,52} may provide a prospective avenue for the long distances beyond 5000 km or so^{53}. It is also noted that the signal photons in our system, centered at 1531.87 nm, both in terms of wavelength and spectral width, are compatible with quantum memory in erbiumdoped materials^{54,55,56}. This, in conjunction with entanglement swapping, constitutes an elementary link of a quantum network, which has been realized recently between two solid states quantum memories^{57,58,59}.
In conclusion, we have demonstrated a quantum teleportation system over metropolitan area, where a 7.1 ± 0.4 Hz teleportation rate is achieved with up to 64 km statetransfer distance. An average fidelity of 86.4 ± 4.5% is measured using QST. Using the DSM, we obtain an average singlephoton fidelity of ≥90.6 ± 2.6%. Our results are further supported by an analytical model which is consistent with measurements of the quantum teleportation system. Finally, our work establishes the possibility of the highspeed quantum information transmission, which serves as a blueprint for the construction of metropolitan quantum network and eventually towards the global quantum internet.
Materials and methods
PPLN module design
The entangled photon pairs are generated using cascaded nonlinear processes of second harmonic generation (SHG) and spontaneous parameter down conversion (SPDC) in a periodically poled lithium niobate (PPLN) waveguide module^{43,60,61}. By fiberintegrating the PPLN waveguide with noiserejecting filters^{61}, the spontaneous Raman scattering noise photons generated in the module are greatly reduced, and entangled photon pairs with a high rate under the same coincidencetoaccidental ratio (CAR) are obtained. More details about parameters of our PPLN module are listed in Supplementary Table S1.
Synchronization
The master clock of the teleportation system is generated from an arbitrary waveform generator (AWG) at Bob and converted into optical pulses by using distributed feedback (DFB) lasers. The optical pulses are sent through the classical channels (CCs) from Bob to Charlie, and from Charlie to Alice. Charlie and Alice receive the optical pulses and convert them into electrical signals using photon detectors (PDs), the outputs of which are used for synchronization at both stations. As shown in Fig. 2, Charlie is connected to Alice and Bob through dark fibers of campus backbone networks. Among them, the fiber that carries photonic qubits is referred to as the quantum channel (QC) and the fiber that transmits optical pulses is referred to as the CC. In addition, both unbalanced interferometers at Alice and Bob are calibrated and stabilized by single photon interference. This method permits us to carry out the preparation and measurement of timebin qubits with stable phases.
Stabilization to ensure the indistinguishability of photon
A successful Bellstate measurement (BSM) relies on the indistinguishability of the two photons, which are generated by independent sources and have been distributed through a 22kmlong fiber channel for each. To do that, the spatial indistinguishability is ensured by using singlemode optical fibers. The spectral indistinguishability of photons from Alice and Bob is ensured by spectral filtering with separate 10GHzwide temperaturestabilized fiber Bragg gratings (FBGs). However, in a realworld quantum teleportation system, the length and birefringence of the optical fiber are influenced by external environments, such as the strain and temperature fluctuations, which make photons distinguishable in degrees of temporal mode and polarization mode. To overcome these challenges, we develop the following experimental techniques to stabilize the QCs (see Supplementary Fig. S4 for the schematic).
Automatic timing control
We measure the arrival times of Alice’s and Bob’s photon respectively, and compensate their time drifts with respect to the system clock. As shown in Fig. 2, the detection signals of photons from the reflection port of the polarization beam splitter (PBS) and the system clock are sent to a timetodigital converter (TDC) to record the arrival times of photons from each channel for every 10 seconds. The drift signals of arrival time in each channel are obtained with a fieldprogrammable gate array (FPGA) circuit. Then the drift signals are fed to two optical variable delay lines (OVDLs, MDL002, General Photonics) in the two QCs to compensate for the arrival time drifts with a resolution of 1 ps. As shown in Fig. 3b, within ~3 h measurement, a time shift of 120 ps (−40 ps) is applied to compensate timing drift in timing through \(\text{Q}{\text{C}}_{\text{A}\to \text{C}}\) (\(\text{Q}{\text{C}}_{\text{B}\to \text{C}}\)), respectively. During the measurement, the minimum count of the HOM interference is 954 ± 37 per 100 s. The result shows that despite the timing drifts in two QCs are much larger than the duration of the singlephoton wavepacket, the teleportation should still succeed with our active timing control.
Automatic polarization control
At Charlie, the photons from Alice and Bob pass through two PBSs so that the polarization indistinguishability between them is naturally satisfied. However, to ensure the minimum loss of photons through PBS, the polarization must be set and maintained, which can be achieved by an automatic polarization control system to compensate for the polarization drifts. In our experiment, we perform automatic polarization control on both \(\text{Q}{\text{C}}_{\text{A}\to \text{C}}\) and \(\text{Q}{\text{C}}_{\text{B}\to \text{C}}\), with schematic setup shown in Supplementary Fig. S4. For instance, to control the polarization of \(\text{Q}{\text{C}}_{\text{A}\to \text{C}}\), we monitor the detection counts of Alice’s photons from the reflection port of the PBS per 10 seconds. The count number is sent to a digital to analog convertor (DAC) circuit, which generates analog feedback signal. The feedback signal is fed to a polarization track module (PTM, POS002, General Photonics), which ensures the maximum counts of the transmission port of the PBS by automatic polarization control. As shown in Fig. 3c, the average fluctuations of \(\text{Q}{\text{C}}_{\text{A}\to \text{C}}\) within ~3 h are limited to 0.2% with our automatic polarization feedback (blue line), and to 15.4% without feedback (red line). The vibrations in the blue line are caused by actively controlling the polarization state of the photons, which recovers within 1 second with our polarization feedback system, as shown in the inset of Fig. 3c.
Data acquisition
Charlie performs \({\psi }^{}{{\rangle }}\) BSM with photonic qubits to be teleported from Alice and idler photons (1549.16 nm) from Bob. When two photons arrive on two different detectors with a time delay of 625 ps, a successful \({\psi }^{}{{\rangle }}\) detection is obtained. Successful BSM results are transmitted through the CC to Bob by classical optical pulses, which are converted back to electrical signals by using a PD. The signals are then sent to a TDC to perform a threefold coincidence measurement with detections of stored signal photons (1531.87 nm) from the outputs of UMZI2 at Bob. The time delay between the BSM result and the detection of signal photons is implemented by using a configurable electronic delay module on the TDC.
Data availability
All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Information. Additional data related to this paper may be requested from the authors.
Change history
28 August 2024
A Correction to this paper has been published: https://doi.org/10.1038/s41377024014420
References
Bennett, C. H. et al. Teleporting an unknown quantum state via dual classical and einsteinpodolskyrosen channels. Phys. Rev. Lett. 70, 1895–1899 (1993).
Kimble, H. J. The quantum internet. Nature 453, 1023–1030 (2008).
Wehner, S., Elkouss, D. & Hanson, R. Quantum internet: a vision for the road ahead. Science 362, eaam9288 (2018).
Long, G. L. et al. An evolutionary pathway for the quantum internet relying on secure classical repeaters. IEEE Netw. 36, 82–88 (2022).
Serafini, A., Mancini, S. & Bose, S. Distributed quantum computation via optical fibers. Phys. Rev. Lett. 96, 010503 (2006).
Bao, X. H. et al. Quantum teleportation between remote atomicensemble quantum memories. Proc. Natl Acad. Sci. USA 109, 20347–20351 (2012).
Nölleke, C. et al. Efficient teleportation between remote singleatom quantum memories. Phys. Rev. Lett. 110, 140403 (2013).
Barrett, M. D. et al. Deterministic quantum teleportation of atomic qubits. Nature 429, 737–739 (2004).
Riebe, M. et al. Deterministic quantum teleportation with atoms. Nature 429, 734–737 (2004).
Reindl, M. et al. Allphotonic quantum teleportation using ondemand solidstate quantum emitters. Sci. Adv. 4, eaau1255 (2018).
Nielsen, M. A., Knill, E. & Laflamme, R. Complete quantum teleportation using nuclear magnetic resonance. Nature 396, 52–55 (1998).
Bouwmeester, D. et al. Experimental quantum teleportation. Nature 390, 575–579 (1997).
Boschi, D. et al. Experimental realization of teleporting an unknown pure quantum state via dual classical and einsteinpodolskyrosen channels. Phys. Rev. Lett. 80, 1121–1125 (1998).
Marcikic, I. et al. Longdistance teleportation of qubits at telecommunication wavelengths. Nature 421, 509–513 (2003).
De Riedmatten, H. D. et al. Long distance quantum teleportation in a quantum relay configuration. Phys. Rev. Lett. 92, 047904 (2004).
Takesue, H. et al. Quantum teleportation over 100 km of fiber using highly efficient superconducting nanowire singlephoton detectors. Optica 2, 832–835 (2015).
Valivarthi, R. et al. Teleportation systems toward a quantum internet. PRX Quantum 1, 020317 (2020).
Ursin, R. et al. Quantum teleportation across the danube. Nature 430, 849–849 (2004).
Landry, O. et al. Quantum teleportation over the swisscom telecommunication network. J. Optical Soc. Am. B 24, 398–403 (2007).
Jin, X. M. et al. Experimental freespace quantum teleportation. Nat. Photonics 4, 376–381 (2010).
Ma, X. S. et al. Quantum teleportation over 143 kilometres using active feedforward. Nature 489, 269–273 (2012).
Yin, J. et al. Quantum teleportation and entanglement distribution over 100kilometre freespace channels. Nature 488, 185–188 (2012).
Sun, Q. C. et al. Quantum teleportation with independent sources and prior entanglement distribution over a network. Nat. Photonics 10, 671–675 (2016).
Valivarthi, R. et al. Quantum teleportation across a metropolitan fibre network. Nat. Photonics 10, 676–680 (2016).
Ren, J. G. et al. Groundtosatellite quantum teleportation. Nature 549, 70–73 (2017).
Li, B. et al. Quantum state transfer over 1200 km assisted by prior distributed entanglement. Phys. Rev. Lett. 128, 170501 (2022).
Xia, X. X. et al. Long distance quantum teleportation. Quantum Sci. Technol. 3, 014012 (2018).
Braunstein, S. L. & Kimble, H. J. Teleportation of continuous quantum variables. Phys. Rev. Lett. 80, 869–872 (1998).
Furusawa, A. et al. Unconditional quantum teleportation. Science 282, 706–709 (1998).
Huo, M. R. et al. Deterministic quantum teleportation through fiber channels. Sci. Adv. 4, eaas9401 (2018).
Zhao, H. et al. Real time deterministic quantum teleportation over 10 km of single optical fiber channel. Optics Express 30, 3770–3782 (2022).
Sychev, D. V. et al. Entanglement and teleportation between polarization and wavelike encodings of an optical qubit. Nat. Commun. 9, 3672 (2018).
Bussières, F. et al. Quantum teleportation from a telecomwavelength photon to a solidstate quantum memory. Nat. Photonics 8, 775–778 (2014).
Pirandola, S. et al. Advances in quantum teleportation. Nat. Photonics 9, 641–652 (2015).
Lu, C. Y. et al. Micius quantum experiments in space. Rev. Modern Phys. 94, 035001 (2022).
Wei, S. H. et al. Towards realworld quantum networks: a review. Laser Photonics Rev. 16, 2100219 (2022).
Hong, C. K., Ou, Z. Y. & Mandel, L. Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett. 59, 2044–2046 (1987).
James, D. F. V. et al. Measurement of qubits. Phys. Rev. A 64, 052312 (2001).
Rubenok, A. et al. Realworld twophoton interference and proofofprinciple quantum key distribution immune to detector attacks. Phys. Rev. Lett. 111, 130501 (2013).
Lo, H. K., Ma, X. F. & Chen, K. Decoy state quantum key distribution. Phys. Rev. Lett. 94, 230504 (2005).
Wang, X. B. Beating the photonnumbersplitting attack in practical quantum cryptography. Phys. Rev. Lett. 94, 230503 (2005).
Ma, X. F. et al. Practical decoy state for quantum key distribution. Phys. Rev. A 72, 012326 (2005).
Yu, H. et al. Spectrally multiplexed indistinguishable singlephoton generation at telecomband. Photonics Res. 10, 1417–1429 (2022).
Wang, X. L. et al. Quantum teleportation of multiple degrees of freedom of a single photon. Nature 518, 516–519 (2015).
Zhang, Q. et al. Experimental quantum teleportation of a twoqubit composite system. Nat. Phys. 2, 678–682 (2006).
Sheng, Y. B., Deng, F. G. & Long, G. L. Complete hyperentangledbellstate analysis for quantum communication. Phys. Rev. A 82, 032318 (2010).
Zhou, L. & Sheng, Y. B. Complete logic bellstate analysis assisted with photonic faraday rotation. Phys. Rev. A 92, 042314 (2015).
Madsen, L. S. et al. Quantum computational advantage with a programmable photonic processor. Nature 606, 75–81 (2022).
Stasi, L. et al. Highefficiency and fast photonnumber resolving parallel superconducting nanowire singlephoton detector. Preprint at https://arxiv.org/abs/2207.14538 (2022).
Anderson, M. et al. Quantum teleportation using highly coherent emission from telecom cband quantum dots. npj Quantum Inf. 6, 14 (2020).
Briegel, H. J. et al. Quantum repeaters: the role of imperfect local operations in quantum communication. Phys. Rev. Lett. 81, 5932–5935 (1998).
Duan, L. M. et al. Longdistance quantum communication with atomic ensembles and linear optics. Nature 414, 413–418 (2001).
Simon, C. Towards a global quantum network. Nat. Photonics 11, 678–680 (2017).
Saglamyurek, E. et al. Quantum storage of entangled telecomwavelength photons in an erbiumdoped optical fibre. Nat. Photonics 9, 83–87 (2015).
Saglamyurek, E. et al. A multiplexed lightmatter interface for fibrebased quantum networks. Nat. Commun. 7, 11202 (2016).
Wei, S. H. et al. Quantum storage of 1650 modes of single photons at telecom wavelength. Preprint at https://arxiv.org/abs/2209.00802 (2022).
Liu, X. et al. Heralded entanglement distribution between two absorptive quantum memories. Nature 594, 41–45 (2021).
LagoRivera, D. et al. Telecomheralded entanglement between multimode solidstate quantum memories. Nature 594, 37–40 (2021).
Hermans, S. L. N. et al. Qubit teleportation between nonneighbouring nodes in a quantum network. Nature 605, 663–668 (2022).
Lefebvre, P. et al. Compact energy–time entanglement source using cascaded nonlinear interactions. J. Optical Soc. Am. B 38, 1380–1385 (2021).
Zhang, Z. C. et al. Highperformance quantum entanglement generation via cascaded secondorder nonlinear processes. npj Quantum Inf. 7, 123 (2021).
Acknowledgements
This work was supported by the National Key Research and Development Program of China (Nos. 2018YFA0307400, 2018YFA0306102), National Natural Science Foundation of China (Nos. 61775025, 91836102, U19A2076, 62005039), Innovation Program for Quantum Science and Technology (No. 2021ZD0301702), Sichuan Science and Technology Program (Nos. 2021YFSY0066, 2021YFSY0062, 2021YFSY0063, 2021YFSY0064, 2021YFSY0065). The authors thank X.X.H, Y.X.L and L.B.Z from the Information Center of the University of Electronic Science and Technology of China (UESTC) for providing access to the campus fiber network and for the help during the experiment.
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Q.Z. conceived and supervised the project. S.S. and C.Y. mainly carried out the experiment and collected the experimental data with help of other authors. H.L., L.Y. and Z.W. developed and maintained the SNSPDs used in the experiment. S.S., C.Y. and Q.Z. analyzed the data. S.S. and Q.Z. wrote the manuscript with inputs from all other authors. All authors have given approval for the final version of the manuscript.
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Shen, S., Yuan, C., Zhang, Z. et al. Hertzrate metropolitan quantum teleportation. Light Sci Appl 12, 115 (2023). https://doi.org/10.1038/s41377023011587
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DOI: https://doi.org/10.1038/s41377023011587
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