Quantum Uncertainties in the Schmidt Basis Given by Decoherence

TL;DR

This paper clarifies that decoherence does not necessarily produce definite eigenstates in the Schmidt basis, showing that such states can still have significant uncertainties, especially in simple Gaussian systems.

Contribution

The paper demonstrates that the Schmidt basis states resulting from decoherence can retain substantial uncertainties, challenging common misconceptions about decoherence producing definite eigenstates.

Findings

Schmidt basis states have similar uncertainties as the full density matrix.

Decoherence does not guarantee eigenstates with minimal uncertainties.

Simple Gaussian systems exemplify persistent quantum uncertainties in the Schmidt basis.

Abstract

A common misconception is that decoherence gives the eigenstates that we observe to be fairly definite about a subsystem (e.g., approximate eigenstates of position) as the elements of the Schmidt basis in which the density matrix of the subsystem is diagonal. Here I show that in simple examples of linear systems with gaussian states, the Schmidt basis states have as much mean uncertainty about position as the full density matrix with its combination of different possibilities.