Space-like separation of entangled quantum states is a central concept in fundamental investigations of quantum mechanics and in quantum communication applications. Optical approaches are ubiquitous in the distribution of entanglement because entangled photons are easy to generate and transmit. However, extending this direct distribution beyond a range of a few hundred kilometres to a worldwide network is prohibited by losses associated with scattering, diffraction and absorption during transmission. A proposal to overcome this range limitation is the quantum repeater protocol, which involves the distribution of entangled pairs of optical modes among many quantum memories stationed along the transmission channel. To be effective, the memories must store the quantum information encoded on the optical modes for times that are long compared to the direct optical transmission time of the channel. Here we measure a decoherence rate of 8 × 10(-5) per second over 100 milliseconds, which is the time required for light transmission on a global scale. The measurements were performed on a ground-state hyperfine transition of europium ion dopants in yttrium orthosilicate ((151)Eu(3+):Y2SiO5) using optically detected nuclear magnetic resonance techniques. The observed decoherence rate is at least an order of magnitude lower than that of any other system suitable for an optical quantum memory. Furthermore, by employing dynamic decoupling, a coherence time of 370 ± 60 minutes was achieved at 2 kelvin. It has been almost universally assumed that light is the best long-distance carrier for quantum information. However, the coherence time observed here is long enough that nuclear spins travelling at 9 kilometres per hour in a crystal would have a lower decoherence with distance than light in an optical fibre. This enables some very early approaches to entanglement distribution to be revisited, in particular those in which the spins are transported rather than the light.

Storing and retrieving a quantum state of light on demand, without corrupting the information it carries, is an important challenge in the field of quantum information processing. Classical measurement and reconstruction strategies for storing light must necessarily destroy quantum information as a consequence of the Heisenberg uncertainty principle. There has been significant effort directed towards the development of devices-so-called quantum memories-capable of avoiding this penalty. So far, successful demonstrations of non-classical storage and on-demand recall have used atomic vapours and have been limited to low efficiencies, of less than 17 per cent, using weak quantum states with an average photon number of around one. Here we report a low-noise, highly efficient (up to 69 per cent) quantum memory for light that uses a solid-state medium. The device allows the storage and recall of light more faithfully than is possible using a classical memory, for weak coherent states at the single-photon level through to bright states of up to 500 photons. For input coherent states containing on average 30 photons or fewer, the performance exceeded the no-cloning limit. This guaranteed that more information about the inputs was retrieved from the memory than was left behind or destroyed, a feature that will provide security in communications applications.

Future multi-photon applications of quantum optics and quantum information science require quantum memories that simultaneously store many photon states, each encoded into a different optical mode, and enable one to select the mapping between any input and a specific retrieved mode during storage. Here we show, with the example of a quantum repeater, how to employ spectrallymultiplexed states and memories with fixed storage times that allow such mapping between spectral modes. Furthermore, using a Ti:Tm:LiNbO3 waveguide cooled to 3 Kelvin, a phase modulator, and a spectral filter, we demonstrate storage followed by the required feed-forward-controlled frequency manipulation with time-bin qubits encoded into up to 26 multiplexed spectral modes and 97% fidelity.PACS numbers: 03.67. Hk, 42.50.Ex, 32.80.Qk, 78.47.jf Further advances towards scalable quantum optics [1,2] and quantum information processing [3,4] rely on joint measurements of multiple photons that encode quantum states (e.g. qubits) [3][4][5]. However, as photons generally arrive in a probabilistic fashion, either due to a probabilistic creation process or due to loss during transmission, such measurements are inherently inefficient. For instance, this leads to exponential scaling of the time required to establish entanglement, the very resource of quantum information processing, as a function of distance in a quantum relay [6]. This problem can be overcome by using quantum memories, which are generally realized through the reversible mapping of quantum states between light and matter [7,8]. For efficient operation, these memories must be able to simultaneously store many photon states, each encoded into a different optical mode, and subsequently (using feed-forward) allow selecting the mapping between input and retrieved modes (e.g., different spectral or temporal modes). This enables making several photons arriving at a measurement device indistinguishable, thereby rendering joint measurements deterministic. For instance, revisiting the example of entanglement distribution, a quantum relay supplemented with quantum memories changes it to a repeater and, in principle, the scaling from exponential to polynomial [4,9].Interestingly, for such multimode quantum memories to be useful, it is not necessary to map any input mode onto any retrieved (output) mode, but it often suffices if a single input mode, chosen once a photon is stored, can be mapped onto a specific output mode (e.g. characterized by the photon's spectrum and recall time) [4,10]. This ensures that the photons partaking in a joint measurement, each recalled from a different quantum memory, are indistinguishable, as required, e.g., for a Bell-state measurement. We emphasize that it does not matter if the device used to store quantum states also allows the mode mapping, or if the mode mapping is performed after recall using appended devices -we will refer to the system allowing storage and mode mapping as the memory.To date, most research assumes photons arriving at different times at the m...