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.
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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 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: | https://discovery.ucl.ac.uk/id/eprint/1504534 |
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