Quantum version of Wielandt's Inequality revisited

Mateusz Michałek and Yaroslav Shitov

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Submission date: 14. Sep. 2018
published in: IEEE transactions on information theory, 65 (2019) 8, p. 5239-5242 
DOI number (of the published article): 10.1109/TIT.2019.2897772
Bibtex
Link to arXiv: See the arXiv entry of this preprint.

Abstract:
Consider a linear space L of complex D-dimensional linear operators, and assume that some power L^k of L is the whole space of D × D matrices. 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).