Fundamental limitations in the purifications of tensor networks
Quantum Physics
2016-07-19 v2
Abstract
We show a fundamental limitation in the description of quantum many-body mixed states with tensor networks in purification form. Namely, we show that there exist mixed states which can be represented as a translationally invariant (TI) matrix product density operator (MPDO) valid for all system sizes, but for which there does not exist a TI purification valid for all system sizes. The proof is based on an undecidable problem and on the uniqueness of canonical forms of matrix product states. The result also holds for classical states.
Keywords
Cite
@article{arxiv.1512.05709,
title = {Fundamental limitations in the purifications of tensor networks},
author = {G. De las Cuevas and T. S. Cubitt and J. I. Cirac and M. M. Wolf and D. Pérez-García},
journal= {arXiv preprint arXiv:1512.05709},
year = {2016}
}
Comments
v1: 11 pages, 1 figure. v2: very minor changes. About to appear in Journal of Mathematical Physics