Purifications of multipartite states: limitations and constructive methods

@article{Cuevas2013PurificationsOM,
  title={Purifications of multipartite states: limitations and constructive methods},
  author={Gemma de las Cuevas and Norbert Schuch and David P'erez-Garc'ia and Juan Ignacio Cirac},
  journal={arXiv: Quantum Physics},
  year={2013}
}
We analyze the description of quantum many-body mixed states using matrix product states and operators. We consider two such descriptions: (i) as a matrix product density operator of bond dimension D, and (ii) as a purification that is written as a matrix product state of bond dimension D'. We show that these descriptions are inequivalent in the sense that D' cannot be upper bounded by D only. Then we provide two constructive methods to obtain (ii) out of (i). The sum of squares (sos… 
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