The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.

Quantum key distribution (QKD) allows two users to communicate with theoretically provable secrecy by encoding information on photonic qubits. Current encoders are complex, however, which reduces their appeal for practical use and introduces potential vulnerabilities to quantum attacks. Distributed-phase-reference (DPR) systems were introduced as a simpler alternative, but have not yet been proven practically secure against all classes of attack. Here we demonstrate the first DPR QKD system with information-theoretic security. Using a novel light source, where the coherence between pulses can be controlled on a pulse-by-pulse basis, we implement a secure DPR system based on the differential quadrature phase shift protocol. The system is modulator-free, does not require active stabilization or a complex receiver, and also offers megabit per second key rates, almost three times higher than the standard Bennett-Brassard 1984 (BB84) protocol. This enhanced performance and security highlights the potential for DPR protocols to be adopted for real-world applications. Quantum key distribution (QKD) has developed strongly since the proposal of the first protocol in 1984 1-3. The future could see widespread quantum networks similar to those in Tokyo 4 and Vienna 5 and global secure communication enabled by QKD over satellites 6. These advances depend on the development of simple, cost-effective and high performance implementations. Innovations in both protocols and system hardware are required to achieve this. Nearly two decades after the inception of Bennett-Brassard 1984 (BB84) 1 , distributed phase reference (DPR) QKD was proposed, allowing for much simpler experimental implementations. The class includes the differential phase shift 7,8 and coherent-one-way 9,10 protocols. One advantage is that the transmitters needed to realize these DPR protocols can be made using off-the-shelf telecom lasers and modulators. However the benefit of their simpler implementation is outweighed by a seriously degraded performance when full security is taken into account 3,11,12. To plug the security gap, two further DPR protocols were proposed: round-robin differential phase shift and differential quadrature phase shift (DQPS). The former simplifies the estimation of Eve's information, but requires an overly complicated QKD receiver setup 13-16 , making it impractical. The latter separates the signal from the differential phase shift protocol into blocks, each having a global phase that varies randomly, ensuring the protocol is immune against coherent attacks 17,18. It does, however, stray from the main goal of DPR protocols to provide simpler QKD implementations, due to the phase randomization requirement that would ordinarily require extra system components. a) Electronic mail: glr28@cam.ac.uk In this work we show it is possible to produce phase coherent and phase randomized pulses from a single device. This device is based on optical injection of one laser diode into another, removing the need for a phase-randomization component in D...

Quantum continuous variables [1] are being explored [2,3,4,5,6,7,8,9,10,11,12,13,14] as an alternative means to implement quantum key distribution, which is usually based on single photon counting [15]. The former approach is potentially advantageous because it should enable higher key distribution rates. Here we propose and experimentally demonstrate a quantum key distribution protocol based on the transmission of gaussian-modulated coherent states (consisting of laser pulses containing a few hundred photons) and shot-noise-limited homodyne detection; squeezed or entangled beams are not required [13]. Complete secret key extraction is achieved using a reverse reconciliation [14] technique followed by privacy amplification. The reverse reconciliation technique is in principle secure for any value of the line transmission, against gaussian individual attacks based on entanglement and quantum memories. Our table-top experiment yields a net key transmission rate of about 1.7 megabits per second for a loss-free line, and 75 kilobits per second for a line with losses of 3.1 dB. We anticipate that the scheme should remain effective for lines with higher losses, particularly because the present limitations are essentially technical, so that significant margin for improvement is available on both the hardware and software.

We consider two quantum cryptographic schemes relying on encoding the key into qudits, i.e., quantum states in a d-dimensional Hilbert space. The first cryptosystem uses two mutually unbiased bases (thereby extending the BB84 scheme), while the second exploits all d 1 1 available such bases (extending the six-state protocol for qubits). We derive the information gained by a potential eavesdropper applying a cloning-based individual attack, along with an upper bound on the error rate that ensures unconditional security against coherent attacks.