Applying computational complexity to the emergence of classicality

TL;DR

This paper explores how computational complexity theory, especially the P versus NP question, can provide new insights into the emergence of classical behavior from quantum systems, contrasting two hypotheses about P versus NP.

Contribution

It introduces a novel perspective linking P versus NP to the quantum-to-classical transition, comparing decoherence-based and complexity-based approaches.

Findings

Decoherence theory aligns with P = NP hypothesis.

Complexity approach assumes P ≠ NP to explain classicality.

Highlights the role of computational complexity in foundational quantum physics.

Abstract

Can the computational complexity theory of computer science and mathematics say something new about unresolved problems in quantum physics? Particularly, can the P versus NP question in the computational complexity theory be a factor in the elucidation of the emergency of classicality in quantum mechanics? The paper compares two different ways of deriving classicality from the quantum formalism resulted from two differing hypotheses regarding the P versus NP question -- the approach of the quantum decoherence theory implying that P = NP and the computational complexity approach which assumes that P is not equal to NP.