Qubits from the classical collision entropy

An orthodox formulation of quantum mechanics relies on a set of postulates in a Hilbert space supplemented with rules to connect it with classical mechanics such as quantization techniques, correspondence principle, etc. Here, we deduce a qubit and its dynamics straightforwardly from a discrete deterministic dynamics and conservation of the classical collision entropy. No Hilbert space is required, although it can be inferred from this approach if necessary.