Unobservables and Decoherence from Complexity

2026-06-18

AI Summary

This work addresses why macroscopic systems exhibit classical behavior and lack quantum interference by examining the role of computational complexity. It argues that if quantum systems cannot efficiently solve NP-complete problems, then certain formally valid quantum measurements are physically unrealizable, rendering the corresponding quantum states either unobservable or inaccessible. By integrating tools from quantum information theory, computational complexity, and linear algebra, the study establishes a direct link between computational constraints and phenomena such as quantum unobservability, state inaccessibility, and decoherence. The authors prove that specific Pauli operators in certain bases are unobservable, demonstrate the absence of physically realizable evolution paths between particular quantum states, and show that some superpositions are empirically indistinguishable from mixed states. These findings suggest that the emergence of classicality at macroscopic scales may stem fundamentally from computational complexity limitations, rather than solely from environmental decoherence.

Abstract

The interface between the quantum and the classical is an intriguing and, at times, hotly contested subject of ongoing research. The quantum regime is characterized by interference, made possible by the superposition principle, while such phenomena are absent in macroscopic, everyday experience. Here, we investigate the link of this absence (or, as we will argue, unobservability) to computational complexity. We show how the assumption that quantum systems cannot solve NP-complete problems efficiently implies that certain formally valid quantum measurements on finite-dimensional systems are unperformable. We study several consequences of this restriction. First, Pauli matrices in an inconveniently transformed basis are a simple example of unobservables. Furthermore, some quantum states are not connected by any physically realizable time evolution. Finally there are quantum states whose coherence cannot be observed, i.e. superpositions of pure quantum states which are indistinguishable from mixtures. We discuss the connection of this phenomenon to the presence of superselection sectors. Our results suggest that the apparent classicality of macroscopic systems may be partly due to limitations on measurements and time evolutions imposed by computational complexity.

Problem

• unobservables
• decoherence
• computational complexity
• quantum-classical transition
• superselection sectors

Innovation

• computational complexity
• unobservables
• decoherence
• superselection sectors
• quantum-classical boundary