Multi-Path Quantum Key Distribution Transport: A Four-Order Mathematical Framework with Provable Zero-Interruption Under Stated Provisioning Conditions

<title>Abstract</title> <p> Metropolitan QKD networks—the Beijing–Shanghai backbone, the Tokyo QKD testbed,and SECOQC—span hundreds of kilometers, yet lack a formally defined, mathematically rigorous transport layer: every deployed network still relies on ad-hoc single-path key management with unpredictable generation rates, unsecured standby pools, and architectures designed for point-to-point links that cannot support multi-hop trusted-relay topologies. This paper provides the first complete transport layer for multi-path QKD networks,built as a four-order progressive mathematical framework: (1) per-path security decou-pling with rigorous Jensen-bound proof; (2) shadow-price optimal multi-path traffic allocation; (3) large-deviation hot-buffer dimensioning with subexponential heavy-tail extension; (4) One Pass Erasable Storage (OPES) cold pools that provably yield zero service interruption under stated provisioning and read-latency axioms. A composable security chain—from Shor–Preskill reduction through multi-path composition to end-to-end ε _total ≤ 10 ⁻⁸ —is established via a formal Security Theorem. A discrete-event simulation on <italic>K = 4</italic> paths across three hops validates the framework across four 3,600-second attack scenarios (baseline, DoS jamming, delay intercept-resend, and combined), with zero service interruptions and address-rotation DoS hit rate matching the theoretical <italic>1/N</italic> bound. The framework is compatible with any QKD protocol satisfying Assumptions A1–A4 and deployable on existing metropolitan fibre infrastructure. </p>