Quantum Version of Wielandt’s Inequality Revisited

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2019
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Shitov, Yaroslav
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10.1109/TIT.2019.2897772
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IEEE Transactions on Information Theory (T-IT) ; 65 (2019), 8. - pp. 5239-5242. - Institute of Electrical and Electronics Engineers (IEEE). - ISSN 0018-9448. - eISSN 1557-9654
Abstract
Consider a linear space L of complex D-dimensional linear operators and assume that some power Lk of L is the whole set End(CD). Perez-Garcia, Verstraete, Wolf, and Cirac conjectured that the sequence L1, L2, . . . stablilizes after O(D2) terms; we prove that this happens after O(D2 log D) terms, improving the previously known bound of O(D4).
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ISO 690MICHALEK, Mateusz, Yaroslav SHITOV, 2019. Quantum Version of Wielandt’s Inequality Revisited. In: IEEE Transactions on Information Theory (T-IT). Institute of Electrical and Electronics Engineers (IEEE). 65(8), pp. 5239-5242. ISSN 0018-9448. eISSN 1557-9654. Available under: doi: 10.1109/TIT.2019.2897772
BibTex
@article{Michalek2019Quant-52489,
  year={2019},
  doi={10.1109/TIT.2019.2897772},
  title={Quantum Version of Wielandt’s Inequality Revisited},
  number={8},
  volume={65},
  issn={0018-9448},
  journal={IEEE Transactions on Information Theory (T-IT)},
  pages={5239--5242},
  author={Michalek, Mateusz and Shitov, Yaroslav}
}
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