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Fundamental limitations in the purifications of tensor networks

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De las Cuevas, G. and Cubitt, J.L. and Wolf, M.M. and Pérez García, David (2016) Fundamental limitations in the purifications of tensor networks. Journal of Mathematical Physics, 57 (7). 071902-071902. ISSN 00222488

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Official URL: http://scitation.aip.org/content/aip/journal/jmp/57/7/10.1063/1.4954983



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.


Item Type:Article
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:39256
Deposited On:07 Oct 2016 12:05
Last Modified:10 Oct 2016 08:42

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