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.
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.
This thesis is concerned with the study and analysis of two quantum cryptographic protocols: quantum key distribution (QKD) and unforgeable quantum money in the continuous-variable (CV) framework. The main advantage of CV protocols is that their implementation only requires standard telecom components. QKD allows two distant parties, Alice and Bob, to establish a secure key, even in the presence of an eavesdropper, Eve. The remarkable property of QKD is that its security can be established in the information-theoretic setting, without appealing to any computational assumptions. Proving the security of CV-QKD protocols is challenging since the protocols are described in an infinite-dimensional Fock space. One of the open questions in CV-QKD was establishing security for two-way QKD protocols against general attacks. We exploit the invariance of Unitary group U(n) of the protocol to establish composable security against general attacks. We answer another pressing question in the field of CV-QKD with a discrete modulation by establishing the asymptotic security of such protocols against collective attacks. We provide a general technique to derive a lower bound on the secret key rate by formulating the problem as a semidefinite program. Quantum money exploits the no-cloning property of quantum mechanics to generate unforgeable tokens, banknotes, and credit cards. We propose a CV private-key quantum money scheme with classical verification. The motivation behind this protocol is to facilitate the process of practical implementation. Previous classical verification money schemes use single-photon detectors for verification, while our protocols use coherent detection.
Quantum key distribution with continuous variables (CV-QKD) enables two parties to share a secret key by using coherent states of light and homodyne detection. This can be carried out by employing low-cost and mature technology developed for telecommunications. It has been shown that at short distances, CV-QKD allows for higher bit rates than conventional discrete variable QKD protocols. Furthermore, CV-QKD could potentially be employed to build a link for secure communication between two parties inside a building or campus and potentially in satellite communications. In this work, we will direct efforts into developing a fiber-based, low-cost, robust, and high-bitrate CV-QKD link. The theoretical concepts, specifics of the QKD system subsequently put into practice in the implementation, have been detailed. Finally, interference experiments have been performed parallel to the proof-of-principle QKD system.
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, or short QKD, aims to establish a secure key withoutmaking any additional assumptions about the abilities or computational power of an adversary who is only limited by the laws of nature. The process of finding a mathematical expression for, or at least a lower bound on, the secure keyrate of some QKD protocol, given relevant system parameters, is called securityproof. In this thesis, we use a recent numerical security proof technique to examine different post selection strategies for continuous-variable quantum key distribution(CV-QKD) protocols with quadrature phase-shift keying modulation and four or eight signal states. CV-QKD protocols use coherent states to encode information and measure the field-quadrature components by homodyne or heterodyne detection. The basic idea of the used numerical security proof technique is to solve thekey rate finding problem in a two-step process. In the first step, the problem is solved approximately, using a numerical algorithm, which yields an upper bound on the secure key rate. This is followed by step two, where the obtained upperbound is converted into a lower bound, using a sequence of theorems and taking numerical errors into account. Postselection aims to increase the secure key rate by removing those parts of the key, where a potential adversary might have gained more information than the communicating parties. The investigations are carried out both for the untrusted ideal and the trusted non-ideal detector scenario and we provide novel analytical results for the operators related to the postselection map.For four-state protocols, we demonstrate that a new cross-shaped postselectionstrategy out performs the state-of-the-art radial postselection scheme clearly in regions of medium to high transmission distances and medium to high values of noise and performs comparable to a more complicated radial&angular scheme. As the error-correction phase is a known bottleneck for many real QKD systems, we examined the secure key rate when a large fraction of the raw key is removed by postselection. We observe that a smart choice of the postselection strategy can increase the key rate while lowering the raw key rate, hence the computational effort in the error-correction phase. One can think this even further: For cross-shaped postselection we showed that the secure key rate is roughly 80% of the secure keyrate without postselection when only 20% of the raw key passes the postselection.For high noise levels this can be increased even further. The cross-shaped post-selection strategy can easily be implemented in the data processing of both new and existing CV-QKD systems, hence can increase the achievable secure key rate significantly. Furthermore, we examined the radial&angular postselection strategy which combines the advantages of the radial postselection scheme for low transmission distances and those of the cross-shaped postselection scheme for medium and high transmission distances on the cost of higher complexity.Additionally, we examine an eight-state phase-shift keying protocol and compare the obtained key rates to the key rates for the four-state protocol and investigate a radial postselection scheme. We observe that the 8PSK protocol yields higher secure key rates and reaches higher maximal achievable transmission distances than a QPSK protocol with a comparable postselection strategy, in particular for medium to high values of excess noise. Furthermore, we explore the relation between the achievable secure key rate and the probability to pass the postselectionphase for various noise-levels and two different practically relevant reconciliation efficiencies. This leads to similar strategies as found for the QPSK protocols to reduce the raw key rate significantly while decreasing the secure key rate only moderately. For very high values of excess noise, the raw key rate can be increased further compared to the key rate achieved without performing postselection whileremoving a large fraction of the raw key rate.
Continuous-variable quantum key distribution (CV-QKD) has emerged as a promising approach for secure quantum communication, offering advantages such as high key generation rates, compatibility with standard telecommunication infrastructure, and potential for integration on photonic chips. This review provides an accessible introduction to the theory of CV-QKD, aimed at researchers entering this rapidly developing field. We focus on fundamental concepts, key protocols, and security analysis essential for understanding CV-QKD systems, with a special emphasis on prepare-and-measure protocols using coherent states under asymptotic security conditions. We explain their equivalence to entanglement-based protocols and detail the security proof framework against collective attacks, encompassing both Gaussian and discrete modulation schemes. We also briefly address more advanced topics, including measurement-device-independent CV-QKD and finite-size security analysis. This work is motivated by Brazil's growing investment in quantum communication technologies. By presenting a clear learning path from basic concepts to advanced topics, this work aims to equip newcomers with the essential tools to engage with current research in CV-QKD, thereby supporting the training of a new generation of researchers in this strategic field.
Quantum key distribution (QKD) is a method that enables two parties separated by distance to share a secret data string. QKD is based on the principles of quantum mechanics and offers information-theoretical security, making it a strong contender for the next generation of cryptography. However, the use of imperfect devices can lead to vulnerabilities and potential quantum hacking schemes. It is crucial to address these imperfections and restore the security of QKD, especially for individuals who use realistic devices for secure communication. QKD can be categorized into two types based on key encoding methods: discrete-variable (DV) QKD and continuous-variable (CV) QKD. It can also be classified based on the transmission medium: fiber-based QKD, free-space-based QKD, and chip-based QKD. This thesis focuses on chip-based DVQKD and fiber-based CVQKD. In the first part, we study the chip-based DVQKD system in the presence of phase-and polarization-dependent loss. We develop innovative methods to restore the security and improve the key rate. The solution is practical, requiring no hardware modifications, and has been adopted by other groups. The second part focuses on fiber-based CVQKD systems that use intensity fluctuating sources. We establish the security by incorporating the concept from DVQKD. Our proposed techniques are practical and do not require any hardware adjustments for existing CVQKD systems. Lastly, we present a general framework for passive CVQKD. Our proposed passive protocol offers a one-time solution to eliminate all potential side channels or imperfections in the source. Interestingly, we discover that the passive source is an excellent choice for the discrete-modulated CVQKD protocol, since the passive protocol offers the same key rate as its active counterpart, while removing all modulator side channels that have plagued the active ones. To sum up, this thesis introduces novel techniques and practical solutions to address imperfections in source devices in different QKD systems. We also propose a passive protocol that can handle all loopholes in source devices in a one-time process. We anticipate that this thesis will facilitate significant advancements in chip-based and fiber-based QKD implementations in the future.