Contextuality without access to a tomographically complete set*

The operational approach to contextuality due to Spekkens requires finding operationally equivalent preparation procedures. Previously these have been obtained by demanding indistinguishably under a set of measurements taken to be tomographically complete. That is, it is taken for granted that the experimenter has access to the full dimension of the system of interest. However, there may in fact be other measurements in the true tomographically complete set, which could break the operational equivalences and hence eliminate the putative contextuality. Here we design tests of contextuality that are immune to this effect for a given number of unknown measurements in the tomographically complete set, allowing contextuality to be demonstrated with weaker assumptions.