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

TL;DR

This paper derives the core principles of quantum mechanics from five information-theoretic axioms, highlighting the unique role of complex Hilbert spaces and ruling out alternative models like real or quaternionic quantum mechanics.

Contribution

It introduces five axioms that derive quantum mechanics from information-theoretic principles, emphasizing the special status of complex Hilbert spaces.

Findings

Axioms I-III are shared with hidden variable theories.

Axiom IV relates to entropy reduction and distinguishes quantum from hidden variable theories.

Axiom V uniquely characterizes complex Hilbert space for qubits.

Abstract

Conventional quantum mechanics with a complex Hilbert space and the Born Rule is derived from five axioms describing properties of probability distributions for the outcome of measurements. Axioms I,II,III are common to quantum mechanics and hidden variable theories. 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.