RT Journal Article
T1 Fundamental limitations in the purifications of tensor networks
A1 De las Cuevas, G.
A1 Cubitt, J.L.
A1 Wolf, M.M.
A1 Pérez García, David
AB 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.
PB American Institute of Physics Inc.
SN 0022-2488
YR 2016
FD 2016
LK https://hdl.handle.net/20.500.14352/24628
UL https://hdl.handle.net/20.500.14352/24628
LA eng
NO European Commission
NO Ministerio de Economía y Competitividad (España)
NO Comunidad de Madrid
DS Docta Complutense
RD 21 dic 2025