Hidden Measurements from Contextual Axiomatics

The hidden measurement approach was originally proposed to show how the tenet of determinism can be upheld in quantum mechanics if one allows the outcome of a measurement to be decided not only by the state of the entity under observation, but also by unkown parameters in the experimental setup. In this paper we show that the structure of hidden measurements is uniquely recovered from three simple axioms and that the state of the entity can be partially defined by the intersection of the sets formed by the closure of each set of measurements that gives rise to a certain outcome.