Classical branch structure from spatial redundancy in a many-body wavefunction

TL;DR

This paper demonstrates that spatial locality constrains the decomposition of many-body wavefunctions into branches, with a maximum record length scale ensuring uniqueness, impacting quantum measurement and thermalization understanding.

Contribution

It provides a formal framework showing how spatial locality and record length scale constrain and potentially guarantee the uniqueness of branch decompositions in many-body quantum systems.

Findings

Branch decompositions are highly constrained by local records.

A maximum record length scale guarantees decomposition uniqueness.

Objective branches may facilitate simulations and understanding of thermalization.

Abstract

When the wavefunction of a large quantum system unitarily evolves away from a low-entropy initial state, there is strong circumstantial evidence it develops "branches": a decomposition into orthogonal components that is indistinguishable from the corresponding incoherent mixture with feasible observations. Is this decomposition unique? Must the number of branches increase with time? These questions are hard to answer because there is no formal definition of branches, and most intuition is based on toy models with arbitrarily preferred degrees of freedom. Here, assuming only the tensor structure associated with spatial locality, I show that branch decompositions are highly constrained just by the requirement that they exhibit redundant local records. The set of all redundantly recorded observables induces a preferred decomposition into simultaneous eigenstates unless their records are highly extended and delicately overlapping, as exemplified by the Shor error-correcting code. A maximum length scale for records is enough to guarantee uniqueness. Speculatively, objective branch decompositions may speed up numerical simulations of nonstationary many-body states, illuminate the thermalization of closed systems, and demote measurement from fundamental primitive in the quantum formalism.