Continuous-variable quantum key distribution systems

Abstract

Quantum Key Distribution (QKD) is capable of supporting ultimate information security. QKD systems can be categorized into two types, namely Discrete Variable QKD (DV-QKD) and Continuous Variable QKD (CV-QKD) systems, but the detectors of CV-QKD exhibit more convenient compatibility with the operational network infrastructure. As a further benefit, CV-QKD is capable of providing a higher key rate than its DV-QKD counterpart, since the associated homodyne or heterodyne detection offers the prospect of high detection efficiency. Therefore, we mainly focus on studying CV-QKD systems. We commence by a brief review of the associated classical post-processing, with an emphasis on Forward Error Correction (FEC)-coded reconciliation schemes. A comprehensive parametric study of Low-Density Parity-Check (LDPC)-coded reconciliation schemes is provided and it is demonstrated that as expected, a longer LDPC code has a better Block Error Rate (BLER) performance and higher reconciliation efficiency, thus offering higher Secret Key Rate (SKR) and longer secure transmission distance. Then the state-of-the-art in both Single-Input Single-Output (SISO) and Multiple- Input Multiple-Output (MIMO) Terahertz (THz) CV-QKD systems is reviewed with an emphasis on the associated quantum transmission part, since the THz band is more tolerant to both weather conditions and atmospheric turbulences than Free Space Optical (FSO) CV-QKD. The SKR versus distance performance reveals that both the thermal noise level, the absorption coefficient and the path loss associated with different frequency bands make a significant difference. In Chapter 3, new near-capacity CV-QKD reconciliation schemes are proposed, where the Authenticated Classical Channel (ClC) and the Quantum Channel (QuC) are protected by separate FEC coding schemes. More explicitly, all of the syndrome-based QKD reconciliation schemes found in literature rely on syndrome-based codes, such as LDPC codes. Hence at the current state-of-the-art the channel codes that cannot use syndrome decoding such as for example the family of Convolutional Codes (CCs) and polar codes cannot be directly applied. Moreover, the ClC used for syndrome transmission in these schemes is typically assumed to be error-free in the literature. To circumvent this limitation, a new codeword-based - rather than syndrome-based - QKD reconciliation scheme is proposed, where Alice sends an FEC-protected codeword to Bob through a ClC, while Bob sends a separate FEC protected codeword to Alice through a QuC. Upon decoding the codeword received from the other side, the final key is obtained by applying a simple modulo-2 operation to the local codeword and the decoded remote codeword. As a result, first of all, the proposed codeword based QKD reconciliation system ensures protection of both the QuC and of the ClC. Secondly, the proposed system has a similar complexity at both sides, where both Alice and Bob have an FEC encoder and an FEC decoder. Thirdly, the proposed system makes QKD reconciliation compatible with a wide range of FEC schemes, including polar codes, CCs and Irregular Convolutional Codes (IRCCs), where a near-capacity performance can be achieved for both the QuC and for the ClC. Our simulation results demonstrate that thanks to the proposed regime, the performance improvements of the QuC and of the ClC benefit each other, hence leading to an improved SKR that inches closer to both the Pirandola-Laurenza-Ottaviani-Banchi (PLOB) bound and to the maximum achievable rate bound. In Chapter 4, the feasibility of CV-QKD is considered in the THz band, experiencing time-varying and frequency-selective fading. Advanced multi-carrier modulation is required for improving the SKR. However, the hostile quantum channel requires powerful classical channel coding schemes for maintaining an adequate reconciliation performance. Against this background, for the first time in the open literature, we propose a multi-carrier quantum transmission regime that incorporates both Orthogonal Frequency Dividion Multiplexing (OFDM) and Orthogonal Time Frequency Space (OTFS) transmission over doubly-selective fading THz channels. Furthermore, we propose a modified Multi-Dimensional Reconciliation (MDR) algorithm for CV-QKD, facilitating the integration of OFDM/ OTFS quantum transmission with LDPC coded key reconciliation. Moreover, we harness Analog Beamforming (ABF) for mitigating the severe THz path loss. Our SKR analysis results demonstrate that the proposed OTFS-based and LDPC-assisted CV-QKD system is capable of outperforming its OFDM counterpart in mobile wireless scenarios. Moreover, we also characterize how improving the MIMO dimension increases the beamforming gain and hence reduces the transmission power required for achieving the secure transmission distance target. Finally, in Chapter 5, the ABF-assisted MIMO OFDM/ OTFS CV-QKD system proposed in Chapter 4 is further developed by harnessing Hybrid Beamforming (HBF). This requires that the full Channel State Information (CSI) is available at both the transmitter ( CSI-T) and receiver ( CSI-R). In order to fulfil this pre-condition in the face of time-varying frequency-selective THz scenarios, a variety of channel estimation methods are conceived for MIMO OFDM/ OTFS systems. SKR analysis results reveal that the HBF MIMO OTFS-based and LDPC-assisted CV-QKD system designed offers higher SKR and longer secure transmission distance than its OFDM-based counterpart. Furthermore, the HBF MIMO OTFS-based system relying on realistic estimated CSI performs similarly to that having perfect CSI in both stationary and mobile scenarios. By contrast, the HBF MIMO OFDM-based system associated with estimated CSI fails to achieve an adequate SKR and secure distance for CV-QKD in mobile scenarios due to its excessive BLER.

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Identifiers

ORCID for Xin Liu: orcid.org/0009-0005-2601-6750

ORCID for Lajos Hanzo: orcid.org/0000-0002-2636-5214

ORCID for Michael Ng: orcid.org/0000-0002-0930-7194

ORCID for Chao Xu: orcid.org/0000-0002-8423-0342

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