Nature cannot be described by any causal theory with a finite number of measurements

We show, for any n ≥ 2, that there exists quantum correlations obtained from performing n dichotomic quantum measurements in a bipartite Bell scenario, which cannot be reproduced by $n-1$ measurements in any causal theory. That is, it requires any no-signaling theory an unbounded number of measurements to reproduce the predictions of quantum theory. We prove our results by showing that there exists Bell inequalities that have to be obeyed by any no-signaling theory involving only $n-1$ measurements and show explicitly how these can be violated in quantum theory. Finally, we discuss the relation of our work to previous works ruling out alternatives to quantum theory with some kind of bounded degree of freedom and consider the experimental verifiability of our results.