Quantum Mereology: Factorizing Hilbert Space into Subsystems with Quasi-Classical Dynamics

TL;DR

This paper proposes a method to decompose Hilbert space into subsystems that exhibit quasi-classical behavior, aiding understanding of the emergence of classicality and spacetime from quantum entanglement.

Contribution

It introduces an algorithm to identify preferred subsystem decompositions based on minimal entanglement growth and localization, without prior structure.

Findings

Algorithm effectively finds quasi-classical decompositions

Pointer states remain localized and robust

Potential implications for spacetime emergence

Abstract

We study the question of how to decompose Hilbert space into a preferred tensor-product factorization without any pre-existing structure other than a Hamiltonian operator, in particular the case of a bipartite decomposition into "system" and "environment." Such a decomposition can be defined by looking for subsystems that exhibit quasi-classical behavior. The correct decomposition is one in which pointer states of the system are relatively robust against environmental monitoring (their entanglement with the environment does not continually and dramatically increase) and remain localized around approximately-classical trajectories. We present an in-principle algorithm for finding such a decomposition by minimizing a combination of entanglement growth and internal spreading of the system. Both of these properties are related to locality in different ways. This formalism could be relevant to the emergence of spacetime from quantum entanglement.