Hilbert-space factorization is a limited and expensive information-processing resource

TL;DR

This paper demonstrates that Hilbert-space factorization is a costly, dissipative process influenced by quantum reference frames, challenging standard decoherence assumptions and providing a new measure for quantum reference frame probabilities.

Contribution

It introduces a framework accounting for the cost of quantum reference frames, revealing limitations of Hilbert-space factorization as an information-processing resource.

Findings

Hilbert-space factorization costs on the order of kT per bit of uncertainty reduction.

Standard decoherence models neglect the dissipative cost of reference frame establishment.

A new measure for the probability of quantum reference frames is proposed.

Abstract

By taking the need for quantum reference frames into account, it is shown that Hilbert-space factorization is a dissipative process requiring on the order of kT to reduce by one bit an observer's uncertainty in the provenance of a classically-recorded observational outcome. This cost is neglected in standard treatments of decoherence that assume that observational outcomes are obtained by interacting with a collection of degrees of freedom identified a priori. Treating this cost explicitly leads to a natural measure of the probability of any particular quantum reference frame.