Derivation of the Rules of Quantum Mechanics from Information-Theoretic Axioms

"Axiom IV recognizes a phenomenon, first noted by Turing and von Neumann, in which the increase in entropy resulting from a measurement is reduced by a suitable intermediate measurement. This is shown to be impossible for local hidden variable theories. Axiom IV, together with the first three, almost suffice to deduce the conventional rules but allow some exotic, alternatives such as real or quaternionic quantum mechanics. Axiom V recognizes a property of the distribution of outcomes of random measurements on qubits which holds only in the complex Hilbert space model. It is then shown that the five axioms also imply the conventional rules for all dimensions."


"Thus, while collapse due to measurement cannot be reproduced by unitary dynamics, a fact that gives rise to the measurement problem, we see that the converse is not true, i.e. unitary dynamics can be reproduced to arbitrary accuracy by a sequence of collapses. It is thus theoretically possible that what appears to us as Schrödinger evolution is a very good approximation to a process in which an interaction Hamiltonian "guides" a sequence of collapse processes happening during very small time intervals. By choosing small enough no increase in entropy would be detected even on a cosmic time scale."

Daniel I. Fivel