The prediction of channel security and maximum transmission distance in Quantum Key Distribution (QKD) networks relies heavily on probabilistic Bell-state fidelity equations and statistical optical attenuation rates. While these stochastic frameworks effectively estimate aggregate signal-to-noise ratios and dark-count probabilities, they fail to deterministically define the exact spatial boundary where localized channel decoherence triggers Entanglement Sudden Death (ESD). This paper introduces a strict continuum framework for quantum optics. By modeling the optical waveguide as a dynamic kinematic balance between the spatial capacity for phase propagation (entanglement distribution) and the localized rate of optical scattering (channel decoherence), we derive a universal critical fidelity radius (Rfidelity). We demonstrate that ESD is not a probabilistic decay over distance, but an exact deterministic limit where localized optical noise strictly overpowers the advective phase-preserving capacity of the surrounding waveguide. We propose a blueprint for Absolute Quantum Repeater Scaling to guarantee 100% unhackable data transmission by engineering node placement around this strict geometric boundary.
The prediction of channel security and maximum transmission distance in Quantum Key Distribution (QKD) networks relies heavily on probabilistic Bell-state fidelity equations and statistical optical attenuation rates. While these stochastic frameworks effectively estimate aggregate signal-to-noise ratios and dark-count probabilities, they fail to deterministically define the exact spatial boundary where localized channel decoherence triggers Entanglement Sudden Death (ESD). This paper introduces a strict continuum framework for quantum optics. By modeling the optical waveguide as a dynamic kinematic balance between the spatial capacity for phase propagation (entanglement distribution) and the localized rate of optical scattering (channel decoherence), we derive a universal critical fidelity radius (Rfidelity). We demonstrate that ESD is not a probabilistic decay over distance, but an exact deterministic limit where localized optical noise strictly overpowers the advective phase-preserving capacity of the surrounding waveguide. We propose a blueprint for Absolute Quantum Repeater Scaling to guarantee 100% unhackable data transmission by engineering node placement around this strict geometric boundary.
The prediction of wavefunction collapse and quantum decoherence in solid-state quantum processors, such as superconducting transmon lattices, relies heavily on the stochastic Lindblad master equation and empirical T1 and T2 relaxation times. While these thermodynamic and statistical frameworks effectively estimate the aggregate probability of quantum error over time, they fail to deterministically define the exact spatial boundary where localized environmental coupling triggers an irreversible collapse of the superposition state. This paper introduces a strict continuum framework for quantum information science. By modeling the topological quantum state as a dynamic kinematic balance between the spatial capacity for phase entanglement (phase coherence) and the localized rate of classical measurement (environmental coupling), we derive a universal critical decoherence radius (Rcollapse). We demonstrate that wavefunction collapse is not a probabilistic decay over time, but an exact deterministic limit where localized environmental perturbation strictly overpowers the advective phase-distributing capacity of the surrounding topological geometry. We propose a blueprint for Absolute Topological Qubit Scaling to guarantee infinite coherence, bypassing massive software-based error-correction overheads.
The impending realization of fault-tolerant quantum computers threatens the foundational public-key cryptography underpinning global telecommunications and financial infrastructure. While algorithmic Post-Quantum Cryptography (PQC) provides mathematical computational hardness against quantum cryptanalysis, Quantum Key Distribution (QKD) establishes an alternative information-theoretically secure physical paradigm based on the immutable laws of quantum mechanics: the No-Cloning theorem and Heisenberg's uncertainty principle. However, deploying scalable, wide-area quantum networks introduces formidable physical and systems engineering challenges: exponential optical fiber attenuation that restricts direct point-to-point QKD to beneath 150 km, high dark-count rates in superconducting nanowire single-photon detectors (SNSPDs), non-deterministic Bell-state entanglement swapping across quantum repeaters, and intense Raman scattering cross-talk when multiplexing quantum channels alongside multi-terabit classical DWDM optical networks. This paper delivers an exhaustive, mathematically formal technical investigation and empirical architectural evaluation of quantum networking and QKD systems. We formalize the asymptotic secret key rate bounds under the Decoy-State BB84 and Measurement-Device-Independent (MDI-QKD) protocols, model continuous entanglement routing over quantum repeaters utilizing bipartite Bell-pair purification, and establish optical co-existence bounds under Dense Wavelength Division Multiplexing (DWDM). Furthermore, we construct an empirical optical testbed evaluating an 8-node metropolitan quantum network co-propagating QKD over 100 Gbps classical optical traffic, paired with hybrid PQC-QKD key derivation functions (ML-KEM + QKD). Our empirical findings demonstrate that decoy-state BB84 achieves a sustainable secret key rate of 1.42 kbps across 100 km of standard single-mode fiber (SMF-28), while hybrid PQC-QKD integration eliminates single-point cryptographic failures with less than 2.4 ms handshake latency overhead. Finally, we formulate open challenges in memory-assisted atomic quantum repeaters, satellite-to-ground freespace entanglement links, and quantum internet transport protocols.
Quantum communications enable secure key transmission and entanglement distribution, but their rates and maximum transmission distances are limited due to the losses and noise introduced by quantum channels. Various techniques have been developed to address these limitations, tailored to the platform and the nature of the decoherence. In this thesis, we explore ways to enhance the performance of quantum communications, with a particular focus on increasing the key rates and transmission distances in quantum key distribution (QKD), a method that leverages quantum mechanics to securely share keys between trusted parties. Additionally, we aim to improve the purity of entangled states shared between two parties, contributing to broader advancements in quantum communications. We begin by introducing a software-enhanced continuous-variable QKD (CV-QKD) protocol, where keys are encoded onto the phase and amplitude degrees of the optical field. This protocol enhances both transmission distance and key rates through a post-selection method employing arbitrary filters, experimentally demonstrated on two different platforms. Its adaptability makes it highly promising, as it can be implemented on existing CV-QKD platforms and dynamically optimises key rates for rapidly changing channels. We then present a protocol for the pure-loss channel leveraging quantum repeaters to mitigate the channel losses by segmenting the total communication distance into smaller, more manageable intervals. This repeater-like protocol introduces a more efficient entanglement-swapping measurement at the repeater station than the state-of-the-art twin-field protocols. Instead of polarisation encoding, our protocol relies on encoding keys in the photon-number basis, optimising the states to achieve the highest key rates for each distance. Notably, this protocol shows strong potential for improving long-distance quantum communication by surpassing the capacity of the direct communication channel at a shorter distance than the existing repeater protocols such as twin-field QKD while achieving an overall higher transmission distance. Finally, in this thesis, we demonstrate that for the Pauli-dephasing channel, placing a node in the middle of the quantum channel to perform a Bell-state measurement as an entanglement-swapping operation does not result in improved key rates, even with reduced decoherence. As a result, we propose an entanglement purification protocol that refines a larger set of noisy entangled states into a smaller set of high-fidelity ones using local operations and classical communication. This purification protocol builds upon earlier purification methods, extending their application from two Bell pairs to any number of Bell pairs and thereby achieving the capacity of the dephasing channel. Through numerous recursive iterations, it produces near-perfect Bell pairs, making it well-suited for quantum repeaters and correcting dephasing errors in quantum computers.
The promise of unconditional security in the Quantum Key Distribution (QKD) depends on the availability of an authenticated classical channel. However, practical implementations often overlook this requirement or rely on computational assumptions that compromise long-term security. To overcome these challenges, this paper presents Entanglement-Based Authenticated Quantum Key Distribution (EAQKD), a novel protocol that addresses critical security and practical limitations in quantum cryptographic key exchange. Our approach integrates quantum entanglement distribution with information-theoretic authentication. We evaluate EAQKD's performance through a comprehensive discrete-event simulation framework modeled on realistic channel characteristics and experimental device parameters. Our modeling incorporates parameters from practical quantum optics setups, including SPDC entanglement sources, superconducting nanowire detectors, and fiber channel imperfections. Our results show quantum bit error rates consistently below the 11% security threshold (ranging from 1.86% at 10 km to 9.27% at 200 km), with secure key rates achieving 1.12×105 bits/s at short distances and maintaining practical rates of 9.8 bits/s at 200 km. When integrated with quantum repeater architectures, our analysis projects that EAQKD can extend secure communication beyond 500 km while providing information-theoretic security guarantees. Comparative analysis against the BB84, E91, and Twin-Field QKD protocols demonstrates EAQKD's superior balance of security, practical performance, and implementation robustness. This work advances quantum cryptography by providing a rigorously analyzed engineering reference for secure key distribution in future quantum communication networks.
Long-distance entanglement distribution is hindered by photon loss in optical fibers and the nocloning theorem. Optical quantum repeater (QR) protocols rely on Bell state measurements (BSMs), they are intrinsically limited to probabilistic photon operations and fail 50% of the time. We propose a hybrid approach to building quantum repeaters that combines the high transmission speed of photonic qubits in optical fiber with the high-fidelity quantum processing capabilities enabled by superconducting circuits. The transduction-enabled superconducting QR (TESQR) architecture eliminates the need for probabilistic BSMs and allows deterministic processing operations. The TESQR framework always yields a final state at the remote nodes rather than aborting on photon loss, manifesting deterministic entanglement distribution within certain parameter regimes. We evaluate the performance by assessing output-state fidelities and success probabilities of entanglement distribution using realistic noise models. Additionally, we integrate an entanglement purification scheme and evaluate the performance through numerical simulations in QuTiP environment. Our results show that, for entanglement swapping, the proposed scheme improves the entanglement distribution rate by an average of 63% and by up to 159% compared with photonic-only architectures. Moreover, after purification, the end-to-end fidelities exceed 0.8 over distances up to 20 km.
Quantum key distribution (QKD) enables information-theoretic secure communication, yet its ultimate tolerance to noise and achievable transmission distance remain fundamentally constrained. We establish the maximum quantum bit error rate (QBER) compatible with secure QKD and derive corresponding upper bounds on communication distance. Our results follow from a fundamental capacity threshold for qubit Pauli channels and apply to protocols based on two or more mutually unbiased bases, using either single-photon or weak coherent sources. By connecting information-theoretic limits to realistic physical noise models, we obtain universal bounds on achievable distances in fiber and free-space links, including diffraction-limited constraints relevant to deep-space quantum communications. These findings clarify the ultimate noise robustness of QKD and delineate the fundamental boundaries of secure quantum communication.