We ask what type of mixed quantum states can arise when a number of separated parties start by sharing a pure quantum state and then this pure state becomes contaminated by noise. We show that not all mixed states arise in this way. This is even the case if the separated parties actively try to degrade their initial pure state by arbitrary local actions and classical communication.
@article{arxiv.quant-ph/0104065,
title = {Are all noisy quantum states obtained from pure ones?},
author = {L. Henderson and N. Linden and S. Popescu},
journal= {arXiv preprint arXiv:quant-ph/0104065},
year = {2009}
}