Quantum theory from questions

Understand

We reconstruct the explicit formalism of qubit quantum theory from elementary rules on an observer's information acquisition.

• Our approach is purely operational: we consider an observer O interrogating a system S with binary questions and define S's state as O's `catalogue of knowledge' about S.
• From the rules we derive the state spaces for N elementary systems and show that (a) they coincide with the set of density matrices over an N-qubit Hilbert space; (b) states evolve unitarily under the group $\rm{PSU}(2^N)$ according to the von Neumann evolution equation; and (c) O's binary questions correspond to projective Pauli operator measurements with outcome probabilities given by the Born rule.
• As a by-product, this results in a propositional formulation of quantum theory.