Quantum key distribution (QKD) enables secure underwater communications essential for maritime infrastructure. Underwater optical channels introduce substantial photon loss (erasures) and ambient noise that degrade QKD performance. This paper investigates whether two four-qubit Calderbank-Shor-Steane (CSS) quantum error correction codes (QECC) mitigate these impairments in vertical underwater communication BB84 QKD protocol. After developing a comprehensive stochastic channel model incorporating photon loss, geometric spreading, and solar noise, we assess the viability of QECC through the analytical study of the quantum bit error rate (QBER) and the secure key rate (SKR) with and without security depending on the signal-to-noise ratio (SNR) validated against Monte Carlo simulations. The standard four-qubit CSS code achieves a 3 dB SNR gain at the QBER 11% security threshold; the discard code variant achieves 4.5 dB. However, QECC includes an encoding overhead that reduces the SKR. We demonstrate a crucial relationship between the SKR and the probability of arrival of the sent photon. Analysis shows that QECC is beneficial exclusively in marginal SNR regimes; at high SNR, raw BB84 dominates. For an ocean Type III Jerlov water scenario with sunlight coming from the sun located at the top of the atmosphere, we identify operational depth-range windows where QECC enables communication otherwise infeasible. This analysis establishes that error correction deployment must be scenario-dependent: extend operational range at the cost of throughput when SNR is marginal, or prioritize key generation rates at high SNR.
Quantum key distribution (QKD) enables secure underwater communications essential for maritime infrastructure. Underwater optical channels introduce substantial photon loss (erasures) and ambient noise that degrade QKD performance. This paper investigates whether two four-qubit Calderbank-Shor-Steane (CSS) quantum error correction codes (QECC) mitigate these impairments in vertical underwater communication BB84 QKD protocol. After developing a comprehensive stochastic channel model incorporating photon loss, geometric spreading, and solar noise, we assess the viability of QECC through the analytical study of the quantum bit error rate (QBER) and the secure key rate (SKR) with and without security depending on the signal-to-noise ratio (SNR) validated against Monte Carlo simulations. The standard four-qubit CSS code achieves a 3 dB SNR gain at the QBER 11% security threshold; the discard code variant achieves 4.5 dB. However, QECC includes an encoding overhead that reduces the SKR. We demonstrate a crucial relationship between the SKR and the probability of arrival of the sent photon. Analysis shows that QECC is beneficial exclusively in marginal SNR regimes; at high SNR, raw BB84 dominates. For an ocean Type III Jerlov water scenario with sunlight coming from the sun located at the top of the atmosphere, we identify operational depth-range windows where QECC enables communication otherwise infeasible. This analysis establishes that error correction deployment must be scenario-dependent: extend operational range at the cost of throughput when SNR is marginal, or prioritize key generation rates at high SNR.
The current literature on quantum key distribution (QKD) is mainly limited to the transmissions over fiber optic, atmospheric or satellite links and are not directly applicable to underwater environments with different channel characteristics. Absorption, scattering, and turbulence experienced in underwater channels severely limit the range of quantum communication links. In the first part of this thesis, we analyze the quantum bit error rate (QBER) and secret key rate (SKR) performance of the well-known BB84 protocol in underwater channels. As path loss model, we consider a modified version of Beer-Lambert formula which takes into account the effect of scattering. We derive a closed-form expression for the wave structure function to determine the average power transfer over turbulent underwater path and use this to obtain an upper bound on QBER as well as a lower bound on SKR. In the second part of this thesis, as a potential solution to overcome range limitations, we investigate a multi-hop underwater QKD where intermediate nodes between the source and destination nodes help the key distribution. We consider the deployment of passive relays which simply redirect the qubits to the next relay node or the receiver without any measurement. Based on the near-field analysis, we present the performance of relay-assisted QKD scheme in terms of QBER and SKR in different water types and turbulence conditions. In the last part of this thesis, we investigate the fundamental performance limits of decoy BB84 protocol over turbulent underwater channels and provide a comprehensive performance characterization. Based on near field analysis, we utilize the wave structure function to determine the average power transfer over turbulent underwater path and use this to obtain a lower bound on key generation rate. Based on this bound, we present the performance of decoy BB84 protocol in different water type.
Abstract Recent advances in quantum communication demand the development of a robust quantum infrastructure for secure data transmission across multimodal networks. Quantum communication transmits information using quantum states (qubits), which act as fundamental units and are vulnerable to noise, decoherence, and hardware imperfections in optical networks. This paper presents a fault-tolerant framework for quantum communication. It integrates Clifford hierarchy-based diagonal gates with Calderbank-Shor-Steane (CSS) codes to ensure error-resilient operation. The proposed scheme uses recursive algebraic structures, including transversal Clifford gates (T, CZ, CCZ). It also employs concatenated Reed-Muller code families to build logical operators that maintain fault tolerance under realistic channel conditions. The recursive algebraic structure of the Clifford hierarchy and the application of quantum Reed-Muller code families in this study provide reliable fault tolerant links and quantum key distribution (QKD) mechanisms for effective noise mitigation. Channel modeling is performed for both fiber-based and free-space optical links, incorporating depolarizing noise, photon loss, and detector dark counts to evaluate system reliability. The Steane and Reed-Muller codes effectively depolarize noise and minimize the logical error rate to an optimum level. Simulation results demonstrate that the proposed coding scheme reduces logical error rates by nearly an order of magnitude compared to unencoded qubits, maintains state fidelity above 0.9 under moderate loss conditions, and achieves secure key rates well beyond the 7% QBER threshold of the conventional BB84 protocol. The results extend the operational noise tolerance of QKD systems under realistic fiber-based conditions and highlight the framework’s adaptability to free-space optical channels. Overall, the developed framework bridges the gap between mathematical fault-tolerant code design and practical quantum communication architectures.
This study compares the quantum bit error rate (QBER) performance of BB84, SARG04, and the entanglement-based BBM92 protocol in non-turbulent underwater optical channels. Clear, coastal, and turbid water types are considered under different background-illumination and receiver configurations. For BB84 and SARG04, channel attenuation and background-induced detections determine the quantum gain and QBER. For BBM92, photon loss is included through the two arm detection efficiencies, whereas the polarization state conditioned on two-photon detection is described by local depolarizing Kraus channels. The BBM92 QBER is obtained from the correlations in both measurement bases and from an exact partition of recorded events into true and false coincidences. Stochastic numerical estimates provide consistency checks of the analytical implementation. The results show that water turbidity and optical background reduce the distance below the adopted QBER threshold. They also show that a low conditional BBM92 QBER may coexist with a very small coincidence probability; therefore, the QBER-threshold distance alone does not represent a complete operational or secret-key-rate bound.
In the quantum key distribution (QKD) process, the presence of noise in the quantum channel reduces the efficiency of QKD with low transmission reliability. Quantum error correcting codes (QECCs) can weaken the impact of noise on the final result due to its flexibility in code length and rate selection. In this paper, QECCs is used to overcome the adverse effects of quantum channel noise, and a QKD protocol based on quantum CSS error correcting codes is proposed. Firstly, we construct the corresponding quantum CSS codes based on classical linear code, then modify and simplify some steps of BB84 protocol by using the characteristics of error correcting codes to design the new protocol. Through theoretical deduction, our QKD protocol based on quantum CSS codes improves the security of key transmission, and the confidentiality of transmission in the noisy quantum channel is also enhanced.
The absence of real single-photon sources is a significant limitation to the experimental implementation of the BB84 quantum key distribution (QKD) protocol. When substantially attenuated laser pulses are substituted for ideal sources in practical systems, the outcome is weak coherent states where each pulse has a nonzero probability of having multiple photons rather than pure single-photon emission. To evaluate quantum bit error rate (QBER), key generation rate and overall system security it is essential to describe the exact impact of the optical and physical system on such pulses. This practical tradeoff presents additional issues. It is crucial to understand how QBER is impacted by attenuation, loss, dispersion, depolarisation and detector properties particularly in adversarial scenarios such as photon number splitting (PNS) and beam-splitting attacks. Although a significant amount of research has been conducted on algorithmic simulations of BB84, there are few complete frameworks that can physically explain these effects and their impact on QBER. This work models the BB84 protocol at the physical level by developing a Python-based simulation platform that takes into account all significant channel impairments and system inefficiencies. The framework supports both theoretical and practical optimisation of QKD systems by further isolating the effects of different optical losses and eavesdropping techniques on QBER and secure key generation.
In the context of secure underwater optical communications, this study examines the performance of the entanglement-based BBM92 protocol when the source generates non-maximally entangled photon pairs. The impact of seawater optical properties, as well as source correlation characteristics, on transmission efficiency is analyzed for three types of nonturbulent channels: clear, coastal, and turbid water. The main performance metrics, including quantum bit error rate (QBER), secret key rate (SKR), and correlation probability, are analytically derived and evaluated as functions of transmission distance between two communicating parties. Monte Carlo simulation results validate our analytical models and quantify performance under different channel conditions.