Operational criterion for controlled dense coding with non-trivial tripartite entangled states

TL;DR

This paper establishes an operational criterion to determine when three-qubit entangled states are useful for controlled dense coding, distinguishing between GHZ-class states that are useful and W-class states that are not.

Contribution

It introduces a classification-based criterion for controlled dense coding usefulness of tripartite entangled states, focusing on GHZ and W classes.

Findings

GHZ-class states are useful for controlled dense coding.

W-class states are not useful for controlled dense coding.

Particular GHZ-class states demonstrate effectiveness in controlled dense coding.

Abstract

In this paper, we provide an operational criterion for controlled dense coding with a general class of three-qubit partially entangled states. A general three-qubit pure entangled state can be classified into two inequivalent classes according to their genuine tripartite entanglement. We claim that if a three-qubit state shows entanglement characteristic similar to $GHZ$-class then such non-trivial tripartite states are useful in {\it controlled dense coding} whereas states belonging to $W$-class are not useful for that. We start with a particular class of non-trivial partially entangled states belonging to $GHZ$-class and show that they are effective in controlled dense coding. Then we cite several other examples of different types of tripartite entangled states to support our conjecture.