Economical(k,m)-threshold controlled quantum teleportation

Abstract

We study a $(k,m)$-threshold controlling scheme for controlled quantum teleportation. A standard polynomial coding over $\text{GF}(p)$ with prime $pgm\ensuremath{-}1$ needs to distribute a $d$-dimensional qudit with $d\ensuremath{\ge}p$ to each controller for this purpose. We propose a scheme using $m$ qubits (two-dimensional qudits) for the controllers' portion, following a discussion on the benefit of a quantum control in comparison to a classical control of a quantum teleportation.