Learning finitely correlated states: stability of the spectral reconstruction

arXiv:2312.07516v2 Announce Type: replace-cross
Abstract: We show that marginals of blocks of $t$ systems of any finitely correlated translation invariant state on a chain can be learned, in trace distance, with $O(t^2)$ copies -- with an explicit dependence on local dimension, memory dimension and spectral properties of a certain map constructed from the state -- and computational complexity polynomial in $t$. The algorithm requires only the estimation of a marginal of a controlled size, in the worst case bounded by …

abstract arxiv cs.et cs.lg map memory quant-ph show stability state systems trace translation type