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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.10003 |
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Table of Contents:
- Set coherence is a basis-independent relational form of quantum coherence: a finite family of quantum states is set incoherent exactly when all its members are diagonal in one common basis. We determine how much low-order Bargmann data are needed to decide this property. For two states, second-order data are complete for qubits but fail for qutrits, while complete third-order data are sufficient for qutrits but fail already in dimension four. We then show that fourth-order, ordering-sensitive Bargmann invariants give the first universal pairwise criterion for set coherence. Applied to all unordered pairs, this criterion yields a complete test for arbitrary finite families. The result provides a low-order hierarchy connecting cyclic trace invariants with the noncommutativity that prevents a common incoherent basis.