Fundamental limitations in the purifications of tensor networks

@article{Cuevas2016FundamentalLI,
  title={Fundamental limitations in the purifications of tensor networks},
  author={G. D. L. Cuevas and T. S. Cubitt and J. Cirac and M. Wolf and D. P{\'e}rez-Garc{\'i}a},
  journal={Journal of Mathematical Physics},
  year={2016},
  volume={57},
  pages={071902}
}
  • G. D. L. Cuevas, T. S. Cubitt, +2 authors D. Pérez-García
  • Published 2016
  • Mathematics, Physics
  • Journal of Mathematical Physics
  • 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… CONTINUE READING
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