The COVID-19 pandemic has increased the interest in the possible causes of the spread of science-based fake news. Indeed, such phenomenon can lead to a generalized distrust of science with serious consequences for our society, ranging from vaccine avoidance to climate change denial. Research in educational psychology has only recently begun to explore the psychological drivers and relationships between misinformation, conspiracy theories and pseudoscientific beliefs. However, existing studies have not focused on specific scientific domains and have involved samples with individuals of different age and sociocultural background. In this empirical study, we focus specifically on the pseudoscientific beliefs of high school students and teachers in a science area where fake news are spreading rapidly on websites and social media, namely, quantum mechanics (QM). To this end, we used a 21-item instrument specifically developed by our group in a previous study to measure pseudoscientific beliefs in QM. The cross-sectional sample included N =1119 high school students (female students=52%) and N=125 high school teachers. The data collected were analyzed using the following methods: confirmatory factor analysis to establish the validity of the instrument; multiple correspondence analysis, to transform categorical variables measuring sociocultural background into continuous variables; repeated measures analysis of variance and linear regression to describe which factors most influence students' and teachers' pseudoscientific beliefs. The results show that, for students, endorsement of pseudoscientific beliefs in QM depends on the following factors: trust in public and science institutions, scientific content consumption, type of high school attended, and QM literacy. For teachers, endorsement of pseudoscientific beliefs in QM depends on the type of degree obtained, QM literacy, perceived usefulness of teaching QM, and confidence in teaching QM. Our study suggests that outreach and popularization interventions for high school students focused on QM, as well as teacher training courses on QM, should also incorporate elements of the nature of science, i.e., on how we develop scientific knowledge, to provide more effective tools to help teachers and students distinguish between correct claims and plausible but false claims, using both prebunking and debunking approaches.