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Fundamental limitations in the purifications of tensor networks

De las Cuevas, G; Cubitt, TS; Cirac, JI; Wolf, MM; Perez-Garcia, D; (2016) Fundamental limitations in the purifications of tensor networks. Journal of Mathematical Physics , 57 (7) , Article 071902. 10.1063/1.4954983. Green open access

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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.

Type: Article
Title: Fundamental limitations in the purifications of tensor networks
Open access status: An open access version is available from UCL Discovery
DOI: 10.1063/1.4954983
Publisher version: http://dx.doi.org/10.1063/1.4954983
Language: English
Additional information: The following article appeared in Journal of Mathematical Physics: G. De las Cuevas, T. S. Cubitt, J. I. Cirac, M. M. Wolf, and D. Pérez-García, Fundamental limitations in the purifications of tensor networks, Journal of Mathematical Physics 2016 57;7 and may be found at http://dx.doi.org/10.1063/1.4954983. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.
Keywords: Science & Technology, Physical Sciences, Physics, Mathematical, Physics, Matrix Product States, Renormalization-Group, Quantum, Systems
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: http://discovery.ucl.ac.uk/id/eprint/1504534
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