Local Classical Strategies vs Geometrical Quantum Constraints

We use an alternative approach to show that quantum entanglement-like correlations cannot be reproduced for any classical protocol. In our proposal, quantum geometric restrictions are impose over the physical system related to the existence of entanglement and we demonstrate that there is no classical local strategy that can reproduce them completely. Typically, the implementations of Bell inequalities have as a starting point the expectation of classical behavior and as conclusion the violation due to the quantum character of the system. We go the other way around. For this purpose, we build a computational simulation based on the scheme of non-communicating students. In this scheme, the students cannot manipulate the quantum systems but they may set up in advance a common strategy and share some common classical data in order to try to reproduce the given quantum correlations of such systems. By thoroughly searching in the whole space of classical strategies we conclude that local operations and classical communications does not satisfy the geometrical constraints imposed by quantum entanglement.