@article{6281907735a24b7ab524b9e0928efacc,
title = "Fundamental limitations in the purifications of tensor networks",
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 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.",
author = "{De las Cuevas}, G. and Cubitt, {T. S.} and Cirac, {J. I.} and Wolf, {M. M.} and D. P{\'e}rez-Garc{\'i}a",
note = "Funding Information: G.D.l.C. and J.I.C. acknowledge support from SIQS. T.S.C. is supported by the Royal Society. M.M.W. acknowledges support from the CHIST- ERA/BMBF project CQC. The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation. DPG acknowledges support from MINECO (Grant Nos. MTM2014-54240-P and ICMAT Severo Ochoa project SEV-2015-0554) and Comunidad de Madrid (Grant No. QUITEMAD+-CM, ref. S2013/ICE-2801). This work was made possible through the support of Grant #48322 from the John Templeton Foundation. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant Agreement No. 648913).",
year = "2016",
month = jul,
day = "1",
doi = "10.1063/1.4954983",
language = "English",
volume = "57",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "American Institute of Physics",
number = "7",
}