Computational Complexity and the Nature of Quantum Mechanics (Extended version)

TL;DR

This paper proposes that quantum mechanics can be understood through two main postulates: logical consistency and polynomial-time computability, explaining quantum paradoxes as conflicts between intractable classical physics and tractable quantum theory.

Contribution

It introduces a novel framework where quantum theory is derived from computational and logical principles, highlighting the role of computational tractability in quantum phenomena.

Findings

Quantum theory follows from logical consistency and polynomial-time inference.

Quantum paradoxes arise from reconciling intractable classical physics with tractable quantum theory.

Entanglement is explained as a consequence of the computational divide.

Abstract

Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from two main postulates (i) the theory should be logically consistent; (ii) inferences in the theory should be computable in polynomial time. The first postulate is what we require to each well-founded mathematical theory. The computation postulate defines the physical component of the theory. We show that the computation postulate is the only true divide between QT, seen as a generalised theory of probability, and classical probability. All quantum paradoxes, and entanglement in particular, arise from the clash of trying to reconcile a computationally intractable, somewhat idealised, theory (classical physics) with a computationally tractable theory (QT) or, in other words, from regarding physics as fundamental rather than computation.