  We illustrate how quantum information theory and free (i.e. noncommutative)
semialgebraic geometry often study similar objects from different perspectives.
We give examples in the context of positivity and separability, quantum magic
squares, quantum correlations in non-local games, and positivity in tensor
networks, and we show the benefits of combining the two perspectives. This
paper is an invitation to consider the intersection of the two fields, and
should be accessible for researchers from either field.
