Detecting mixed-unitary quantum channels is NP-hard

Colin Do-Yan Lee; John Watrous

doi:10.22331/q-2020-04-16-253

Detecting mixed-unitary quantum channels is NP-hard

Colin Do-Yan Lee and John Watrous

Institute for Quantum Computing and School of Computer Science, University of Waterloo, Canada

Published:	2020-04-16, volume 4, page 253
Eprint:	arXiv:1902.03164v3
Doi:	https://doi.org/10.22331/q-2020-04-16-253
Citation:	Quantum 4, 253 (2020).

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Abstract

A quantum channel is said to be a $\textit{mixed-unitary}$ channel if it can be expressed as a convex combination of unitary channels. We prove that, given the Choi representation of a quantum channel $\Phi$, it is NP-hard with respect to polynomial-time Turing reductions to determine whether or not $\Phi$ is a mixed-unitary channel. This hardness result holds even under the assumption that $\Phi$ is not within an inverse-polynomial distance (in the dimension of the space upon which $\Phi$ acts) of the boundary of the mixed-unitary channels.

► BibTeX data

@article{Lee2020detectingmixed,
  doi = {10.22331/q-2020-04-16-253},
  url = {https://doi.org/10.22331/q-2020-04-16-253},
  title = {Detecting mixed-unitary quantum channels is {NP}-hard},
  author = {Lee, Colin Do-Yan and Watrous, John},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {253},
  month = apr,
  year = {2020}
}

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Cited by

[1] Mark Girard, Debbie Leung, Jeremy Levick, Chi-Kwong Li, Vern Paulsen, Yiu Tung Poon, and John Watrous, "On the mixed-unitary rank of quantum channels", arXiv:2003.14405.

[2] Cristhiano Duarte, Barbara Amaral, Marcelo Terra Cunha, and Matthew Leifer, "Investigating Coarse-Grainings and Emergent Quantum Dynamics with Four Mathematical Perspectives", arXiv:2011.10349.

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[4] Uma Girish, Ran Raz, and Wei Zhan, "Quantum Logspace Algorithm for Powering Matrices with Bounded Norm", arXiv:2006.04880.

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