How can question answering (QA) systems determine whether a query is ambiguous? Ambiguity detection is essential in open-domain QA, as misclassification leads to either answering under the wrong interpretation or triggering unnecessary clarification. However, existing methods conflate answer diversity with ambiguity, leading to inaccurate predictions. They also process all queries uniformly, resulting in wasteful computation. We propose ARCHIVE, an accurate and efficient framework that detects ambiguity via *logical conflict*: a query is ambiguous if its valid answers cannot all be true under a single interpretation. ARCHIVE combines a lightweight early-exit encoder for surface-detectable cases with a conflict modeling module that captures logical relations among answers, reinforced by an invariance objective for robustness to noisy answer sets. We also present QuireQA, a 4,703-query benchmark spanning factoid, non-factoid, and ill-formed queries. Experiments show that ARCHIVE outperforms competitors, improving F1-amb and F1-unamb by up to 10.4 and 21.6 points, respectively, while operating 16× faster than the best competitor.