Quantum communication with $SU(2)$ invariant separable $2\times N$ level systems

Information is encoded in a qubit in the form of its Bloch vector. In this paper, we propose protocols for remote transfers of information in a known and an unknown qubit to qudits using $SU(2)$- invariant $\frac{1}{2}\otimes S$ discordant states as a channel. These states have been identified as separable equivalents of the two-qubit entangled Werner states in [Bharath & Ravishankar, Phys. Rev. A 89, 062110]. Due to $SU(2) \times SU(2)$ invariance of these states, the remote qudit can be changed by performing appropriate measurements on the qubit. We also propose a protocol for transferring information of an unknown qudit to a remote qudit using a $\frac{1}{2}\otimes S$- state as a channel. Finally, we propose a protocol for swapping of quantum discord from $\frac{1}{2}\otimes S$- systems to $S\otimes S$- systems. All the protocols proposed in this paper involve separable states as quantum channels. Employing these protocols, we believe that quantum information processing can be performed using highly mixed separable higher dimensional states.