Quantum physics challenges our views of the physical world and describes phenomena that cannot be directly observed. The use of language is hence essential in the teaching of quantum physics. With a sociocultural view of learning, we investigate characteristics of preuniversity students' small-group discussions and their potential for enhancing understanding of quantum physics. The empirical data are 96 small-group discussions about two fundamental dilemmas: whether light can be both waves and particles, and whether the cat in Schrödinger's thought experiment can be considered to be both dead and alive. The discussions were analyzed by means of a framework of four categories, grouped as productive and nonproductive for learning, where "productive" means that students build constructively on each other's utterances and take the peers' ideas into account. Results show that a total of 70% of the discussions were productive, indicating that small-group discussions have a potential for enhancing understanding in quantum physics. This potential is constituted by leading students to (i) articulate conceptual difficulties, (ii) deepen their understanding through exchange of views, and (iii) formulate new questions. The paper concludes with a discussion on how the learning potential of small-group discussions may be realized by combining dialogic and authoritative approaches.