Study of controlled dense coding with some discrete tripartite and quadripartite states

The paper presents a detailed study of controlled dense coding scheme for different types of three and four-particle states. It consists of GHZ state, GHZ type states, maximal slice (MS), state, 4-particle GHZ state and W class of states. It is shown that GHZ-type states can be used for controlled dense coding in a probabilistic sense. We have shown relations among parameter of GHZ type state, concurrence of the shared bipartite state by two parties with respect to GHZ type and Charlie's measurement angle θ. The GHZ states as a special case of MS states, depending on parameters, have also been considered here. We have seen that tripartite W state and quadripartite W state cannot be used in controlled dense coding whereas |Wn〉ABC states can be used probabilistically. Finally, we have investigated controlled dense coding scheme for tripartite qutrit states.