Hilbert-space factorization is a limited and expensive information-processing resource
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.
Cite
@article{arxiv.1401.4767,
title = {Hilbert-space factorization is a limited and expensive information-processing resource},
author = {Chris Fields},
journal= {arXiv preprint arXiv:1401.4767},
year = {2014}
}
Comments
8 pages; Comment on M. Tegmark, "Consciousness as a state of matter" (arXiv:1401.1219); v2: 12 pages, cleaned up notation, added a figure, expanded discussion of quantum Darwinism and related factorization entropy to the measure problem