Quantum version of Wielandt's Inequality revisited
Commutative Algebra
2018-09-13 v1
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 DxD matrices. Perez-Garcia, Verstraete, Wolf and Cirac conjectured that the sequence L^1,L^2,... stablilizes after O(D^2) terms; we prove that this happens after O(D^2 log(D)) terms, improving the previously known bound of O(D^4).
Keywords
Cite
@article{arxiv.1809.04387,
title = {Quantum version of Wielandt's Inequality revisited},
author = {Mateusz Michałek and Yaroslav Shitov},
journal= {arXiv preprint arXiv:1809.04387},
year = {2018}
}