Wavefunction branching: when you can't tell pure states from mixed states

TL;DR

This paper introduces a new way to define wavefunction branchings, which are quantum superpositions indistinguishable from mixed states, and explores their implications for quantum-to-classical transition and quantum information processing.

Contribution

It provides a novel, interpretation-independent definition of wavefunction branchings based on local gate complexity, and analyzes their properties and implications in many-body quantum states.

Findings

Branchings are hard to distinguish from mixed states without active error correction.

Branchings tend to grow further apart over time under natural evolution.

Branchings are associated with effective irreversibility and absorption of entanglement.

Abstract

We propose a definition of wavefunction "branchings": quantum superpositions which can't be feasibly distinguished from the corresponding mixed state, even under time evolution. Our definition is largely independent of interpretations, requiring only that it takes many more local gates to swap branches than to distinguish them. We give several examples of states admitting such branch decompositions. Under our definition, we argue that attempts to get relative-phase information between branches will fail without frequent active error correction, that branches are effectively the opposite of good error-correcting codes, that branches effectively only grow further apart in time under natural evolution, that branches tend to absorb spatial entanglement, that branching is stronger in the presence of conserved quantities, and that branching implies effective irreversibility. Identifying these branch decompositions in many-body quantum states could shed light on the emergence of classicality, provide a metric for experimental tests at the quantum/ classical boundary, and allow for longer numerical time evolution simulations. We see this work as a generalization of the basic ideas of environmentally-induced decoherence to situations with no clear system/ environment split.