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Do experiments based on superconducting loops segmented with Josephsonjunctions (e.g., flux qubits) show macroscopic quantum behavior in the sense ofSchr\"odinger's cat example? Various arguments based on microscopic andphenomenological models were recently adduced in this debate. We approach thisproblem by adapting (to flux qubits) the framework of large-scale quantumcoherence, which was already successfully applied to spin ensembles andphotonic systems. We show that contemporary experiments might show quantumcoherence more than 100 times larger than experiments in the classical regime.However, we argue that the often-used demonstration of an avoided crossing inthe energy spectrum is not sufficient to make a conclusion about the presenceof large-scale quantum coherence. Alternative, rigorous witnesses are proposed.

Insufficiency of avoided crossings for witnessing large-scale quantum coherence in flux qubits