This paper aims at supporting the claim that some forms of hyper-simplification, by making physics seem easy, are at risk of dangerously distorting the content as well as the process of learning physics. The paper presents examples of dangerous simplifications in the teaching of quantum physics. Then, examples of productive forms of complexity are discussed, both as criteria for designing teaching proposals, and for realizing appropriate learning environments, namely properly complex territories. Empirical results, from a teaching/learning experiment on quantum physics at upper secondary school (grade 13), are reported. These results show examples of students' reactions to travelling through a complex territory, and allow us to argue that unavoidable difficulty in learning quantum physics can be transformed into cultural challenges within reach of secondary school students.