One of the most peculiar features of quantum mechanics is the exponential growth of resources required to define the quantum state of a composite system. It makes it the direct simulation of even a handful of particles impossible in practice. This growth is due to the fact that the quantum state contains the full statistical information about the probabilities of any possible event. Since the quantum state is not a physically accessible observable, but can be statistically reconstructed only by performing many measurements on different replicas, it is natural to wonder if this resource excess is strictly necessary to describe the actual state of a single realization. The quantum probabilities could be reproduced by a theory where a single system carries less information than the quantum state. So, is the exponential complexity an intrinsic property of quantum systems or of the formalism? Is it possible to reduce the complexity in the single system representation by changing the formalism? These questions and their relation with quantum communication complexity are the main subject of my research.