Quantum from principles

TL;DR

This paper reconstructs quantum theory from six foundational principles within a framework of information theories, showing it as the optimal theory for controlling randomness, thus providing a logical basis for quantum mechanics.

Contribution

It introduces six principles that uniquely derive quantum theory from information-theoretic rules, moving away from ad hoc assumptions.

Findings

Reconstructed quantum features from principles

Derived the Hilbert space framework logically

Characterized quantum as maximal control of randomness

Abstract

Quantum theory was discovered in an adventurous way, under the urge to solve puzzles-like the spectrum of the blackbody radiation-that haunted the physics community at the beginning of the 20th century. It soon became clear, though, that quantum theory was not just a theory of specific physical systems, but rather a new language of universal applicability. Can this language be reconstructed from first principles? Can we arrive at it from logical reasoning, instead of ad hoc guesswork? A positive answer was provided in Refs. [1, 2], where we put forward six principles that identify quantum theory uniquely in a broad class of theories. We first defined a class of "theories of information", constructed as extensions of probability theory in which events can be connected into networks. In this framework, we formulated the six principles as rules governing the control and the accessibility of information. Directly from these rules, we reconstructed a number of quantum information features, and eventually, the whole Hilbert space framework. In short, our principles characterize quantum theory as the theory of information that allows for maximal control of randomness.