The maximal transmission distance of optical quantum communication is reaching a hard limit imposed by the intrinsic loss of the transmission medium, e.g. optical fibre. A quantum repeater promises to push that limit towards much longer, potentially intercontinental distances. Its implementation relies on the development of efficient and long-lived quantum memories that can store and retrieve the quantum properties of light. Sources of photonic entanglement, tailored for quantum memories, are also necessary and represent a challenging experimental task.

I will review the efforts of our group towards the realization of quantum memories based on rare-earth-ion doped crystals (REIC) as well as a matching source of photon pair. This approach has recently allowed us to demonstrate several features that are of great importance for quantum repeaters, and for quantum networks in general.

After a brief introduction, I will show how we have successfully entangled two neodymium-doped crystals in a heralded fashion. I will then show how polarization qubits encoded in true single photons can be stored in such crystals, despite their intrinsic birefringence and polarization-dependant absorption. I will finally present an on-demand quantum memory exploiting the long hyperfine coherence time of europium ions to store light for up to 8 ms. Our results highlight the great potential of REIC for quantum repeaters.

The ability to send quantum information encoded in photons over large distances is hampered by the unavoidable loss in the communication channel. In classical communication, channel-loss is alleviated by amplifying the information carrier, however, due to the no-cloning theorem for quantum states, this approach is not viable for quantum communication channels. Instead long-distance quantum communication can be enabled by quantum-repeaters, which serve to distribute entanglement over the entire channel by means of entanglement swapping between subdivision of the channel [1]. In order to synchronize the process of entanglement swapping between adjacent subdivisions, quantum repeaters must incorporate quantum memories [2]. A quantum memory is a device that has the ability to (reversibly) map quantum states between photons and atoms [3]. In most of the quantum repeater architectures proposed to date, it is required that quantum memories feature recall on demand. Other desirable attributes of a quantum memory are high fidelity and efficiency, long storage times, and the possibility to simultaneously store multiple carriers of quantum information, i.e. record multiple photonic modes. The combination of a quantum state storage protocol based on an atomic frequency comb (AFC) [4] with rare-earth-ion doped crystals cooled to cryogenic temperatures as storage materials [5] has been shown to meet many of these requirements. In particular, it is well suited for storage of temporally multiplexed photons [6,7]. Yet, despite first proof-of-principle demonstrations [8], recalling the quantum information at a desired time (i.e. read-out on demand) with broadband, single-photon-level pulses remains an outstanding challenge. Fortunately, the AFC protocol allows not only for multimode storage in the time domain, but also in the frequency domain.

Here, we will present the first experimental demonstration of frequency-multiplexed storage of attenuated laser pulses followed by read-out on demand in the frequency domain, pointing to a quantum repeater architecture based on frequency multiplexing. Our work is based on the AFC protocol and employs a Tm-doped LiNbO3 waveguide cooled to 4 K [9,10]. Using a serrodyne sideband chirping technique we prepare several frequency-combs in the atomic absorption spectrum. Each section of AFC is a few 100 MHz wide and since we vary the comb-tooth spacing in each section we prepare them with different storage times on the order of 20-150 ns. After the AFC preparation, we send a probe pulse, which is modulated to contain several frequency components that correspond to the centre frequencies of the AFC sections. The mean photon number in each mode is set to be around one. As the probe pulse is mapped to our quantum memory the different frequency modes are mapped to different sections of the AFC and thus recalled at different times. The recalled pulses pass through a frequency filter with a bandwidth matching a single frequency mode. Before frequency filtering we are able to impart again a frequency shift on the recalled pulses, which can hence be set to pass the spectral filter. This constitutes recall on demand of a particular frequency mode. Our multimode quantum memory is highly flexible and can be set to recall all modes at the same time, and adapted to broader or narrower frequency modes. In addition it has been shown to faithfully store time bin qubits in pure and entangled states and preserve all degrees of freedom of the photonic wavefunction [9,11].

Finally, we will argue that, in view of a quantum repeater, our approach based on a multimode memory with read-out on demand in the frequency domain is equivalent to temporal multiplexing and read-out on demand in the temporal domain. This overcomes one further obstacle to building quantum repeaters using rare-earth-ion doped crystals as memory devices.

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[2] N. Sangouard, et al., Rev. Mod. Phys., 83(1), 33 (2011)
[3] A. I. Lvovsky, B. C. Sanders, and W. Tittel, Nat. Photon, 3(12), 706 (2009)
[4] M. Afzelius, et al., Phys. Rev. A, 79(5), 052329 (2009)
[5] W. Tittel, et al., Laser & Photonics Rev., 4(2), 244 (2010)
[6] I. Usmani, et al., Nat Commun, 1 (2010)
[7] M. Bonarota, J.-L. Le Gouët, and T. Chanelière, New J. of Phys., 13(1), 013013 (2011)
[8] M. Afzelius, et al., Phys. Rev. Lett., 104, 040503 (2010)
[9] E. Saglamyurek, et al., Nature, 469(7331), 512 (2011)
[10] N. Sinclair, et al., J. of Luminescence, 130(9), 1586 (2010)
[11] E. Saglamyurek, et al., Phys. Rev. Lett., 108, 083602 (2012)

Quantum theory and the relativistic no-signalling principle both give ways of controlling information, in the sense that someone who creates information somewhere in space-time can rely on strict limits both on how much information another party can extract and on where they can obtain it. An increasingly long list of interesting cryptographic applications exploit the power of the no-signalling principle as well as the properties of quantum information. I describe recent work in this area, including secure protocols for bit commitment, quantum tagging (quantum position authentication) and new intrinsically relativistic cryptographic tasks.

A fundamental task in modern cryptography is the joint computation of a function which has two inputs, one from Alice and one from Bob, such that neither of the two can learn more about the other's input than what is implied by the value of the function. In this work we show that any quantum protocol for the computation of a classical deterministic function that outputs the result to both parties (two-sided computation) and that is secure against a cheating Bob can be completely broken by a cheating Alice. Whereas it is known that quantum protocols for this task cannot be completely secure, our result implies that security for one party implies complete insecurity for the other. Our findings stand in stark contrast to recent protocols for weak coin tossing, and highlight the limits of cryptography within quantum mechanics. We remark that our conclusions remain valid, even if security is only required to be approximate.

Apart from their foundational signicance, entropic uncertainty relations play a central role in proving the security of quantum cryptographic protocols. Of particular interest are thereby relations in terms of the smooth min-entropy for BB84 and six-state encodings. Previously, strong uncertainty relations were obtained which are valid in the limit of large block lengths. Here, we prove a new uncertainty relation in terms of the smooth min-entropy that is only marginally less strong, but has the crucial property that it can be applied to rather small block lengths. This paves the way for a practical implementation of many cryptographic protocols. As part of our proof we show tight uncertainty relations for a family of Renyi entropies that may be of independent interest.

Quantum steering allows two parties to verify shared entanglement even if one measurement device is untrusted, as well as convincing an unbelieving party of the existence of entanglement. I will discuss quantum steering in the contexts of recent experiments [1,2,3] steering the polarization degree of freedom for single photons. The historical context as well as modern motivation for steering will be covered, as well as the similarities and differences in the various recent experiments.

Our own work [1], demonstrating quantum steering with high efficiency (62%) in two measurement bases, will be discussed in detail, including the technical challenges in certifying the results due to measurement imperfections of various types. We ultimately demonstrate a violation of some 48 standard deviations of the steering inequality most relevant to applications, which also happens to be the one most difficult to violate. The efficiency demonstrated in this experiment (62%) is half again as high as the previous world record for detection efficiency for an experiment in this context.

I will conclude with our current research project – to implement semi-device-independent quantum key distribution [4], with security guaranteed by a steering inequality. This lies in the gap between current QKD implementations and the ultimate security given by device-independent QKD, and, in practical situations, requires a detection efficiency some 10% higher again than our previous result, which should be achievable given the advances made since that result was published.

1. DH Smith, G Gillett et al., Nat. Commun. 3:625 (2012)
2. AJ Bennet et al., Phys. Rev. X 2, 031003 (2012)
3. B Wittmann, S Ramelow et al., New J. Phys. 14, 053030 (2012)
4. C Branciard et al., Phys. Rev. A 85, 010301(R) (2012)

We show that the maximum transmission distance of continuous-variable quantum key distribution in presence of a Gaussian noisy lossy channel can be arbitrarily increased using a heralded noiseless linear amplifier. We explicitly consider a protocol using amplitude and phase modulated coherent states with reverse reconciliation. Assuming that the secret key rate drops to zero for a line transmittance T_lim, we find that a noiseless amplifier with amplitude gain g can improve this value to T_lim/g², corresponding to an increase in distance proportional to log g.