Optimal quantum channel for perfect controlled super-dense coding protocol

Abstract

Perfect super-dense coding protocol allows transmission of two classical bits (cbits) by sending just one quantum bit (qubit) with unit success probability. Perfect controlled super-dense coding protocol should be such that perfect super-dense coding is achieved with the controller's cooperation. There are different possible types of quantum channels to be shared among the authorized parties to perform perfect controlled super-dense coding. Of our interest is the quantum channel which is optimal in the sense that no cbits can be transmitted with certainty without the controller's cooperation. We attack this problem by means of the so-called control power. By calculating and analyzing the control power for specific quantum channels we figure out the one that is optimal. We also address the issue of how to prepare such optimal quantum channel.