Information Conservation and the Emergence of Complex Quantum Amplitudes

This paper derives the complete mathematical structure of quantum mechanics—complex Hilbert spaces, unitary evolution, and Born-rule probabilities—from five information-theoretic axioms, without assuming quantum mechanics at the outset. Starting from an ontology of microhistories (fully specified microscopic trajectories), we define branches as equivalence classes of operationally indistinguishable microhistories. We then show that five physically motivated constraints on how information is stored, mixed, and transformed uniquely force the effective state space to be a complex projective space with unitary dynamics.