Proof of the Holevo--Utkin conjecture on sharp ${\ell }_p$ norms for zero-sum vectors

Haonan Zhang

Let $d\ge 3$ and $p>0$. Let $\Vert x{\Vert }_p$ denote the ${\ell }_p$ (quasi-)norm of a $d$-dimensional vector $x$. Holevo and Utkin \cite{HU26} conjectured that for $0<p\le 1$, \[ \min \left\…