Appears in collection : Random Tensors / Tenseurs aléatoires
Motivated by considerations from quantum information theory, we study the asymptotic behaviour of large tensor powers of normed spaces and of operators between them. We define the tensor radius of a finite-dimensional normed space $\mathrm{X}$ as the limit of the sequence $A_{k}^{1 / k}$, where $A_{k}$ is the equivalence constant between the projective and injective norms on $X^{\otimes} k$. We show in particular that Euclidean spaces are characterized by the property that their tensor radius equals their dimension. Joint work with Alexander Müller-Hermes, arXiv:2110.12828
By Dario Trevisan
By Jussi Behrndt
By Ronnie Pavlov
By Tamara Kucherenko
