Network operators migrating distributed systems to post-quantum and quantum-safe cryptography face a resource-management problem: quantum key distribution (QKD) gives the strongest guarantee available but is hardware-scarce and costly, so only a fraction of a deployment's links can receive it. Default practice -- ranking links by traffic or centrality and upgrading the top scorers -- optimizes each link in isolation, while a distributed job's real security is set by whichever active link ends up weakest. We present WLPA (Weakest-Link Posture Assignment), an implementation-ready decision framework and algorithm for allocating scarce quantum-safe postures under hardware, latency, and compliance constraints. WLPA computes the optimal weakest-link posture in closed form and returns an assignment in O(|E| log |E|) time -- 125 ms for a 20,000-link network on a laptop -- with a breach-aware refinement matching an exact integer program under common conditions. Our central contribution is a dichotomy telling operators exactly when existing per-link heuristics already match this optimum and when they systematically fail: under constant upgrade cost and uniform traffic-driven risk the two coincide exactly; once costs vary or an adversary concentrates on weak targets, heuristics leave the weakest link unprotected, unboundedly. We validate WLPA across 19 experiments: four microservice topologies, a real enterprise network (SNAP email-Eu-core), a post-quantum latency benchmark, a Qiskit BB84 simulation and a real-hardware BB84 run on IBM's ibm_marrakesh processor, checks against real production traffic traces, a CVE-calibrated correlated-compromise study, Bayesian uncertainty quantification, and seven baseline methods. A concrete-security reduction grounds the framework as theoretical foundation, not primary contribution.

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