Memory cost of quantum contextuality

The simulation of quantum effects requires certain classical resources, and quantifying them is an important step to characterize the difference between quantum and classical physics. For a simulation of the phenomenon of state-independent quantum contextuality, we show that the minimum amount of memory used by the simulation is the critical resource. We derive optimal simulation strategies for important cases and prove that reproducing the results of sequential measurements on a two-qubit system requires more memory than the information-carrying capacity of the system.