Information-theoretic postulates for quantum theory

TL;DR

This paper reconstructs quantum theory using four natural information-theoretic postulates, explaining why quantum mechanics has its mathematical structure and exploring potential modifications.

Contribution

It introduces a reconstruction of quantum theory based solely on information-theoretic principles, avoiding reliance on the traditional mathematical formalism.

Findings

Quantum theory can be derived from four natural postulates.

The postulates relate to correlations, information equivalence, reversible evolution, and positivity.

The approach provides insights into possible modifications of quantum mechanics.

Abstract

Why are the laws of physics formulated in terms of complex Hilbert spaces? Are there natural and consistent modifications of quantum theory that could be tested experimentally? This book chapter gives a self-contained and accessible summary of our paper [New J. Phys. 13, 063001, 2011] addressing these questions, presenting the main ideas, but dropping many technical details. We show that the formalism of quantum theory can be reconstructed from four natural postulates, which do not refer to the mathematical formalism, but only to the information-theoretic content of the physical theory. Our starting point is to assume that there exist physical events (such as measurement outcomes) that happen probabilistically, yielding the mathematical framework of "convex state spaces". Then, quantum theory can be reconstructed by assuming that (i) global states are determined by correlations between local measurements, (ii) systems that carry the same amount of information have equivalent state spaces, (iii) reversible time evolution can map every pure state to every other, and (iv) positivity of probabilities is the only restriction on the possible measurements.