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

TL;DR

This paper investigates controlled dense coding protocols using various tripartite and quadripartite quantum states, analyzing their effectiveness and probabilistic capabilities for quantum communication.

Contribution

It provides a comprehensive analysis of controlled dense coding with multiple multipartite states, including GHZ, W, and qutrit states, highlighting their probabilistic utility.

Findings

GHZ-type states can be used probabilistically for controlled dense coding.

W states generally cannot be used for controlled dense coding.

Certain W_n states are useful probabilistically in controlled dense coding.

Abstract

The paper presents the detailed study of controlled dense coding scheme for different types of $3$ and $4-$ particle states. It consists of GHZ state, GHZ type states, Maximal Slice state, Four 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 $\theta$. We have seen that tripartite W state and quadripartite W state cannot be used in controlled dense coding whereas $\vert W_{n}\rangle_{ABC}$ states can be used probabilistically. Finally, we have investigated controlled dense coding scheme for tripartite qutrit states.