Quantum key distribution is a technique in which secret key bits are encoded into quantum states which are transmitted over a quantum channel, e.g. an optical link, so that the security is guaranteed by the laws of quantum physics. Most experimental realizations to date have relied on discrete protocols, involving ideally single-photons states (or, in practice, strongly attenuated light pulses) as well as single-photon detectors. In this chapter, we present an overview of the recent continuous-variable quantum cryptosystems, which instead rely on continuously-modulated Gaussian states (e.g. coherent states) and homodyne detection. The series of security proofs of these protocols against increasingly powerful attacks will be reviewed. A particular emphasis will be put on the op-timality of Gaussian attacks in this context, which holds provided that the second-order moments of the relevant variables are monitored.
Quantum key distribution is a technique in which secret key bits are encoded into quantum states which are transmitted over a quantum channel, e.g. an optical link, so that the security is guaranteed by the laws of quantum physics. Most experimental realizations to date have relied on discrete protocols, involving ideally single-photons states (or, in practice, strongly attenuated light pulses) as well as single-photon detectors. In this chapter, we present an overview of the recent continuous-variable quantum cryptosystems, which instead rely on continuously-modulated Gaussian states (e.g. coherent states) and homodyne detection. The series of security proofs of these protocols against increasingly powerful attacks will be reviewed. A particular emphasis will be put on the op-timality of Gaussian attacks in this context, which holds provided that the second-order moments of the relevant variables are monitored.
Quantum key distribution (QKD) enables the establishment of secret keys between users connected via a channel vulnerable to eavesdropping, with information-theoretic security, that is, independently of the power of a malevolent party [1]. QKD systems based on the encoding of the key information on continuous variables (CV), such as the values of the quadrature components of coherent states [2], [3], present the major advantage that they only require standard telecommunication technology. However, the most general security proofs for CVQKD required until now the use of Gaussian modulation by the transmitter, complicating practical implementations [4]–[6]. Here, we experimentally implement a protocol that allows for arbitrary, Gaussian-like, discrete modulations, whose security is based on a theoretical proof that applies generally to such situations [7]. These modulation formats are compatible with the use of powerful tools of coherent optical telecommunication, allowing our system to reach an estimated performance of tens of megabit per second secret key rates over 25 km
Quantum Key Distribution (QKD) provides a method for securely sharing a secret key between two distant parties, Alice and Bob, by leveraging the principles of quantum mechanics. This thesis focuses on Continuous-Variable (CV) QKD, a variant of QKD where information is encoded in the quadrature components of coherent light states, allowing for efficient and cost-effective detection using homodyne or heterodyne receivers. The thesis is divided into three main parts: an introduction to quantum cryptography concepts, the presentation of a CV-QKD protocol, and a detailed security proof of the protocol against different types of attacks. The security proof considers both finite and infinite symbol transmission and tackles various eavesdropping attacks, including individual, collective, and coherent attacks. The use of Gaussian states and operations provides a promising approach to enhance QKD security, particularly in the context of practical quantum cryptography. The final sections provide a mathematical framework for the optimization of secure key rates and strategies for addressing the photon-number cutoff assumption in practical implementations.
Continuous variable quantum key distribution with discrete modulation has the potential to provide information-theoretic security using widely available optical elements and existing telecom infrastructure. While their implementation is significantly simpler than that for protocols based on Gaussian modulation, proving their finite-size security against coherent attacks poses a challenge. In this work we prove finite-size security against coherent attacks for a discrete-modulated quantum key distribution protocol involving four coherent states and heterodyne detection. To do so, and contrary to most of the existing schemes, we first discretize all the continuous variables generated during the protocol. This allows us to use the entropy accumulation theorem, a tool that has previously been used in the setting of discrete variables, to construct the finite-size security proof. We then compute the corresponding finite-key rates through semi-definite programming and under a photon-number cutoff. Our analysis provides asymptotic rates in the range of 0.1 − 10 − 4 bits per round for distances up to hundred kilometres, while in the finite case and for realistic parameters, we get of the order of 10 Gbits of secret key after n ∼ 10 11 rounds and distances of few tens of kilometres.
Quantum key distribution (QKD) protocols allow two trusted parties to distribute a cryptographic key which they can further use for the unconditionally secure classical communication. During the last decades the field has grown mature with the commercial prototypes being available. They mostly rely on the faint laser pulses implementing the protocols on the basis of single qubits and qubit pairs. Alternatively, the continuous-variable (CV) protocols based on the multi-photon states of light were developed recently. They are typically built using the quadrature modulation of the coherent or squeezed states and subsequent homodyne detection. In the case of Gaussian modulation the security of the protocols is based on the extremality of Gaussian states, which allows estimating bounds on the leaked information. The Gaussian CV QKD protocols were shown secure for any degree of channel attenuation, but are restricted by the channel noise. Moreover, the applicability of Gaussian CV QKD protocols is limited by the effectiveness of classical post-processing algorithms, used by the trusted parties to process the measured data and distill the cryptographic key. On the other hand, the squeezedstate CV QKD protocols were previously considered ineffective under limited degrees of squeezing, while strong squeezing remains experimentally challenging. In the present work we distinguish between the classical and quantum resources in the Gaussian CV QKD and address the role of nonclassicality in the Gaussian protocols. We demonstrate, that by properly combining squeezed resource and coherent modulation, trusted parties are able to decouple eavesdropper from the channel, thus being able to establish the secure key from any amount of the classical mutual information. Our result shows a very promising path towards the long-distance CV QKD.
Quantum continuous variables (CV) have been explored as an alternative to qubits for quantum key distribution (QKD). More specifically, protocols using coherent states and homodyne or heterodyne measurements have been proposed and experimentally demonstrated (Grosshans et al., 2003). Relying on technologies allowing much higher rates than allowed by the single photon detectors used in qubit based QKD, those protocols are the only ones which could allow key rates in the GHz range in the foreseeable future. Furthermore, their security proofs have recently been extendend to generic attacks in the case of gaussian modulation. However, to our knowledge, all security analyses up to know have implicitely assumed Bob's measurement setup to use a homo- or heterodyne detection with an external classical phase reference, while the experimental realizations use a lightbeam for this role. This beam doesn't carry any information useful to the spy, and any attack on its phase could equally be carried on the signal beam. However, the intensity of this beam is used in experimental implementations to calibrate the quantum noise level. This calibration is then used to determine the channel gain, which is an important parameter of Eve's attack. We show that this allows Eve to implement an intercepte resend attack forbiding QKD as soon as the losses are above 3dB. We also give simple countermeasures to this new class of attacks.
Quantum information processing with continuous variables is a paradigm that has attracted a growing interest over the past years, partly as a consequence of the prospects for high-rate quantum communication systems based on standard optical telecommunication components. In this overview article, we introduce the concept of quantum continuous variables in optics and then turn to the fundamental impossibility of cloning continuous-variable light states, a result that lies at the heart of quantum key distribution. Then we present state-of-the-art quantum key distribution systems relying on continuous variables, focusing mainly on the protocols using Gaussian-modulated coherent light states and emphasizing the current experimental demonstration of these systems. Finally, we briefly review recent security proofs of these cryptographic protocols.