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MiS Preprint
79/2018
Quantum version of Wielandt's Inequality revisited
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 $D\times D$ matrices. Perez-Garcia, Verstraete, Wolf and Cirac conjectured that the sequence $L^1,L^2,\dots$ stablilizes after $O(D^2)$ terms; we prove that this happens after $O(D^2 \log(D))$ terms, improving the previously known bound of $O(D^4)$.
