Complexity of mixed states in QFT and holography

@article{Cceres2020ComplexityOM,
  title={Complexity of mixed states in QFT and holography},
  author={Elena C{\'a}ceres and Shira Chapman and Josiah D. Couch and Juan Hernandez and Robert C. Myers and Shan-Ming Ruan},
  journal={Journal of High Energy Physics},
  year={2020},
  volume={2020},
  pages={1-120}
}
We study the complexity of Gaussian mixed states in a free scalar field theory using the ‘purification complexity’. The latter is defined as the lowest value of the circuit complexity, optimized over all possible purifications of a given mixed state. We argue that the optimal purifications only contain the essential number of ancillary degrees of freedom necessary in order to purify the mixed state. We also introduce the concept of ‘mode-by- mode purifications’ where each mode in the mixed… 
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