An arbitrary unknown quantum state cannot be measured precisely or replicated perfectly 1 . However, quantum teleportation enables unknown quantum states to be transferred reliably from one object to another over long distances 2 , without physical travelling of the object itself. Long-distance teleportation is a fundamental element of protocols such as large-scale quantum networks 3,4 and distributed quantum computation 5, 6 . But the distances over which transmission was achieved in previous teleportation experiments, which used optical fibres and terrestrial free-space channels [7] [8] [9] [10] [11] [12] , were limited to about 100 kilometres, owing to the photon loss of these channels. To realize a global-scale 'quantum internet' 13 the range of quantum teleportation needs to be greatly extended. A promising way of doing so involves using satellite platforms and space-based links, which can connect two remote points on Earth with greatly reduced channel loss because most of the propagation path of the photons is in empty space. Here we report quantum teleportation of independent single-photon qubits from a ground observatory to a low-Earthorbit satellite, through an uplink channel, over distances of up to 1,400 kilometres. To optimize the efficiency of the link and to counter the atmospheric turbulence in the uplink, we use a compact ultrabright source of entangled photons, a narrow beam divergence and high-bandwidth and high-accuracy acquiring, pointing and tracking. We demonstrate successful quantum teleportation of six input states in mutually unbiased bases with an average fidelity of 0.80 ± 0.01, well above the optimal state-estimation fidelity on a single copy of a qubit (the classical limit) . Our demonstration of a ground-to-satellite uplink for reliable and ultra-long-distance quantum teleportation is an essential step towards a global-scale quantum internet. In our experiment, the quantum state to be teleported is the polari zation of a single photon: | χ〉 1 = α| H〉 1 + β| V〉 1 , where α and β are unknown complex numbers satisfying | α| 2 + | β| 2 = 1, and | H〉 and | V〉 denote the horizontal and vertical polarization states, respectively, which can be used to encode the basic logic states | 0〉 and | 1〉 for a quantum bit (qubit), and the subscript '1' labels the photon. Such a single qubit is generated at an observatory ground station in Ngari, Tibet (32° 19′ 33.07″ N, 80° 1′ 34.18″ E, altitude of 5,047 m), with the aim of teleporting it to the Micius satellite that was launched from China on 16 August 2016 to an altitude of about 500 km. The satellite flies along a Sunsynchronous orbit; that is, it passes over any given point on Earth's surface at the same local solar time (00:00). Quantum teleportation 2 relies on using both a classical channel and a quantum channel (entanglement), shared between the two communicating parties; we refer to these parties as Ngari and Micius. The entangled state of a pair of photons can be written as , one of the four maximally entan gled twoqubit Bell states (here photon 2 is at Ngari and photon 3 is at the satellite). Ngari performs a joint measurement on the photon that is to be teleported (photon 1) and one of the photons from the entangled pair (photon 2), projecting them into one of the four Bell states. When the Bellstate measurement yields , the other photon from the entan gled pair (photon 3) carries exactly the desired state. If another Bell state, φ , is detected, then the state of photon 3 is equivalent to the original state of photon 1, up to a unitary π phase shift in the data postprocessing. The experimental realization of quantum teleportation of an inde pendent single photon necessitates the simultaneous creation of two entangled photon pairs 15 and highvisibility quantum interference between them 7 . The multiphoton coincidence count rate is several orders of magnitude lower than in typical single or twophoton experiments. Owing to the complexity of the multiphoton setup for spacetogroundscale quantum teleportation, we choose the uplink configuration (Fig. 1a) in which the transmitter (Ngari) is placed in the ground station and the receiver (Micius) is in the satellite. To maximize the count rate in the experiment, we prepare compact and ultrabright fourphoton sources (Fig. 1b) . Ultraviolet femtosecond pulses (with a central wavelength of 390 nm, pulse width of 160 fs and repetition rate of 80 MHz) from a modelocked Ti:sapphire laser pass through two bismuth borate (BiBO) crystals to generate two pairs of photons. The first pair is generated via collinear spontaneous parametric down conversion (SPDC), whereby one of the photons is detected as a trigger to herald the presence of photon 1 (count rate of 5.7 × 10 5 s −1 ), whose state is to be teleported. Using a halfwave plate (HWP) and a quarterwave plate (QWP), the initial polarization state of photon 1 can be arbitrarily prepared. The second BiBO crystal was aligned for noncollinear SPDC 16 and prepared in the frequencyuncorrelated polarizationentangled state | φ + 〉 23 , with a count rate of 1 × 10 6 s −1 and a fidelity of 0.933 measured on the ground (see Methods). To realize the Bellstate measurement, photons 1 and 2 are then over lapped on a polarizing beam splitter (PBS), which transmits H and reflects V polarization. After the PBS, we select the events that corre spond to each output detecting one photon, which is possible only if the two photons have the same polarization-| H〉 1 | H〉 2 or | V〉 1 | V〉 2 -thus projecting the wave function into a subspace of φ | 〉 = | 〉 | 〉 ±| 〉 | 〉 / ±
In REF , the authors demonstrated the quantum teleportation of independent single-photon qubits over 1,400 kilometres.
Ground-to-satellite quantum teleportation
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