Quantum cloning transformation unlocks the potential of W class of states in a quantum secure direct communication protocol

TL;DR

This paper introduces a novel controlled quantum secure direct communication protocol using W class states, demonstrating how quantum cloning machines can retrieve secrets and analyzing success probabilities linked to entanglement and state parameters.

Contribution

The work presents the first controlled QSDC protocol based on W class states and explores how quantum cloning enhances secret retrieval and protocol efficiency.

Findings

Success probability is related to entanglement in W states.

Quantum cloning machine efficiency can be optimized using shared state parameters.

Less entangled W states can still effectively facilitate secure communication.

Abstract

In a controlled quantum secure direct communication (Controlled QSDC) protocol between three parties, the sender sends the encoded secured message to one of the two receivers, which can be decoded only when the other receiver agrees to cooperate. A lot of studies have been done on it using the three-qubit GHZ state, and only a few works have involved the W state. In this work, we introduce a controlled QSDC protocol exploiting a three-qubit W class of state shared between three parties, Alice (Sender), Bob (Controller), and Charlie (Receiver). In the proposed protocol, the shared state parameters and the secret are linked in such a way that it is very difficult to factor them. We will show that these parameters can be factored out easily if the receiver uses a quantum cloning machine (QCM) and thus can retrieve the secret. We find that the protocol is probabilistic and have calculated the probability of success of the protocol. Further, we establish the relation between the success probability and the efficiency of the QCM. In general, we find that the efficiency of the constructed QCM is greater than or equal to $\frac{1}{3}$, but we have shown that its efficiency can be enhanced when the parameters of the shared state are used as the parameters of the QCM. Moreover, we derived the linkage between the probability of success and the amount of entanglement in the shared W class of state. We analyzed the obtained result and found that even a less entangled W class of state can also play a vital role in the proposed controlled QSDC scheme.