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 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.
Abstract We address the crucial role of noisy squeezing in security and performance of continuous-variable (CV) quantum key distribution (QKD) protocols. Squeezing has long been recognized for its numerous advantages in CV QKD, such as enhanced robustness against channel noise and loss, and improved secret key rates. However, the excess noise of the squeezed states, that unavoidably originates already from optical loss as well as other imperfections in the source, raises concerns about its potential exploitation by an eavesdropper. For the widely adopted trust assumption on the excess noise in the signal states, we confirm the stability of the protocol against the noisy squeezing in both purely attenuating as well as noisy channels in the asymptotic limit, which implies perfect parameter estimation. In the finite-size regime we show that this stability largely holds at up to 107 data points using optimal biased homodyne detection for key distribution and parameter estimation. Untrusted assumption on the noisy squeezing, on the other hand, introduces additional security bounds on the squeezing excess noise already in the asymptotic regime, which is further enforced by the finite-size effects. Additionally, we show the critical negative role of noisy squeezing in the case of atmospheric free-space channels, already in the trusted-noise and asymptotic assumptions, which emphasizes the importance of squeezing purity in the free-space quantum channels. Our results pave the way towards practical realization of squeezed-state CV QKD protocols in both fibre and free-space channels.
Abstract We address the crucial role of noisy squeezing in security and performance of continuous-variable (CV) quantum key distribution (QKD) protocols. Squeezing has long been recognized for its numerous advantages in CV QKD, such as enhanced robustness against channel noise and loss, and improved secret key rates. However, the excess noise of the squeezed states, that unavoidably originates already from optical loss as well as other imperfections in the source, raises concerns about its potential exploitation by an eavesdropper. For the widely adopted trust assumption on the excess noise in the signal states, we confirm the stability of the protocol against the noisy squeezing in both purely attenuating as well as noisy channels in the asymptotic limit, which implies perfect parameter estimation. In the finite-size regime we show that this stability largely holds at up to 107 data points using optimal biased homodyne detection for key distribution and parameter estimation. Untrusted assumption on the noisy squeezing, on the other hand, introduces additional security bounds on the squeezing excess noise already in the asymptotic regime, which is further enforced by the finite-size effects. Additionally, we show the critical negative role of noisy squeezing in the case of atmospheric free-space channels, already in the trusted-noise and asymptotic assumptions, which emphasizes the importance of squeezing purity in the free-space quantum channels. Our results pave the way towards practical realization of squeezed-state CV QKD protocols in both fibre and free-space channels.
Quantum key distribution (QKD) is fundamentally different from most classical key distribution schemes, such as Diffie-Hellman key exchange, in the sense that no computational complexity assumption is required on the power of adversaries to prove its security. QKD relies on basic laws of quantum physics and it is proven that it can enable highly secure data communication. Such achievements, however, are facing technological problems that have to be resolved in order to provide a viable solution to a large group of customers. While there are discrete-variable QKD schemes, which rely on encoding data in discrete degrees of freedom, such as polarization of single photons, in this thesis, we focus on the continuous-variable QKD (CV-QKD) protocols, in which data is encoded on the quadratures of light. Currently, one of the major drawbacks of CV-QKD is its poor performance at long distances. Nevertheless, such a limitation in CV-QKD can be overcome with the assistance of quantum repeaters that rely on entanglement distillation via noiseless linear amplifiers (NLAs). Such systems can, in principle, offer large secret key rates over long distances. In this thesis, we aim to provide a realistic analysis of a CV-QKD protocol running over quantum scissors (QSs) as realistic NLAs. We will report the obstacles that one could face in realizing CV-QKD in such a scenario. A review of CV-QKD and QS-based NLAs will be given, based on which QS-assisted CV-QKD is proposed. We, particularly, focus on the modelling of the QSs' structure and their effect on the secret key rate aiming to find operational regimes where the performance of the QKD scheme is enhanced. This study paves the way for implementing long-distance CV-QKD protocols that rely on QS/NLA devices over CV quantum repeaters. \n \nIn this thesis, we also consider and account for a realistic analysis of a CV-QKD protocol with non-Gaussian modulation, which is assisted by the means of QSs. We will show that, while we have to deal with similar obstacles as in the Gaussian modulation, we can potentially improve performance of the non-Gaussian modulation protocol. \n \nAs an alternative approach to extend the secure distance of CV-QKD protocols, the last part of this thesis is devoted to presenting realistic threat models for satellite QKD, wherein we consider several eavesdropping scenarios by limiting eavesdroppers' access to the trusted ground and/or satellite stations. In such scenarios, the eavesdropper has only limited access to the sender and/or receiver stations. \nFor example, we will explore the case where an eavesdropper can only receive an attenuated version of the transmitted signals. As well, we will focus on the case where Eve's signals would reach the receiver via a lossy channel inaccessible to the eavesdropper. We show that, in the case of both Gaussian and non-Gaussian protocols, this limitation would allow trusted parties to achieve higher key rates than what can be achieved when unrestricted eavesdropping is possible.
A continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) protocol using squeezed states is proposed where the two legitimate partners send Gaussian-modulated squeezed states to an untrusted third party to realize the measurement. Security analysis shows that the protocol can not only defend all detector side channels, but also attain higher secret key rates than the coherent-state-based protocol. We also present a method to improve the squeezed-state CV-MDI QKD protocol by adding proper Gaussian noise to the reconciliation side. It is found that there is an optimal added noise to optimize the performance of the protocol in terms of both key rates and maximal transmission distances. The resulting protocol shows the potential of long-distance secure communication using the CV-MDI QKD protocol.
Quantum information processing uses the laws of quantum physics to perform tasks that are infeasible or impossible classically. Within this broader programme, quantum communication has emerged as one of the most practically mature sub-fields of quantum information science, with several proposed protocols having already been demonstrated over deployed optical fibre and free-space links. Of the various platforms available for encoding quantum information for communication, the continuous-variable (CV) framework encodes information in the quadratures of the electromagnetic field and is therefore directly compatible with the existing machinery of classical coherent optical communications. The most prominent CV protocol is continuous-variable quantum key distribution (CV-QKD), which establishes an information-theoretically secure cryptographic key between two spatially separated parties. Because CV-QKD reuses much of the hardware of classical coherent telecommunications, including off-the-shelf lasers, modulators, and balanced detectors, it is a leading candidate for the deployment of quantum-secured communication over standard optical fibre networks. The development of CV-QKD has typically proceeded with the underlying physics dictating the engineering. Security proofs, often relying on the Gaussian optimality of collective attacks, set the structure of the protocol, and the practical system is then built to satisfy the assumptions on which those proofs depend. Contributions of this thesis adopt the opposite view, taking the practical engineering of high-rate CV-QKD systems as the starting point and developing the theoretical machinery required to support it. The first contribution is the formalisation of one-round sliced reconciliation with guard-band post-selection as a key distillation scheme designed for real-time, high-throughput operation. Originally introduced experimentally as a means to stabilise bit error rates and enable the use of fixed-rate error correction codes at high symbol rates, guard-band post-selection is shown here to identify the guard-band span as a free parameter that can be tuned to hold the quantum bit error rate approximately constant across a range of channel conditions. However, conditioning on accepted data produces non-Gaussian post-selected statistics that lie outside the reach of standard Gaussian-optimality security arguments, which motivates the remaining two contributions. The second contribution is an asymptotic security analysis of guard-band post-selected CV-QKD against arbitrary collective attacks, no longer restricted to Gaussian adversaries. By using a quantum channel estimate as side information and by lifting reduced-state distances to purification distances via entropic continuity bounds, security is certified against the class of channels lying close to a Gaussian thermal-loss reference, with a key-rate penalty that scales with the energy-constrained diamond distance to that reference. The third contribution is the experimental basis required to apply this framework in practice. A lightweight three-stage protocol for quantum channel estimation is proposed and demonstrated, which repurposes the Gaussian probe constellation already present in the CV-QKD signal and requires no additional hardware or modifications to the underlying protocol. Over single-mode optical fibre at distances from 10 km to 50 km, the protocol produces physically valid process tensor estimates whose energy-constrained diamond distances to a Gaussian reference channel remain on the order of 10^(-3) throughout. Together, these three contributions provide a treatment of post-selected Gaussian-modulated CV-QKD in which the engineering, the security theory, and the channel characterisation are designed to operate together within a deployable system.
We address the robustness of quantum key distribution protocols to imperfections of a quantum channel. Starting from the Gaussian continuous-variable protocols we recapitulate the role of quadrature squeezing in providing security of the key in the noisy channels taking into account the limited efficiency of data processing. We then develop a model of channel noise that allows an equivalent quantification as for the continuous-variable protocols and apply it to the discrete-variable protocols. This allows us to perform the comparison of robustness of the protocols to the channel noise when either continuous- or discrete-variable coding is used. We show that while continuous-variable protocols enforced by arbitrarily strong nonclassicality demonstrate some quantitative advantage in the channels with relatively low losses, the discrete-variable protocols can achieve better tolerance to the channel noise even when using the limited nonclassical resource. The result is promising for planning of integrated secure communication systems.