Quantum cloning transformation unlocks the potential of W class of states in a secret sharing protocol

• URL: http://arxiv.org/abs/2408.06722v1
• Date: Tue, 13 Aug 2024 08:27:58 GMT
• Title: Quantum cloning transformation unlocks the potential of W class of states in a secret sharing protocol
• Authors: Rashi Jain, Satyabrata Adhikari,
• Abstract summary: We introduce a quantum secret sharing protocol exploiting a three-qubit W class of state shared between three parties. We find that the protocol is probabilistic and have calculated the probability of success of the protocol. Even a less entangled W class of state can also play a vital role in the proposed secret-sharing scheme.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: One of the most challenging problems is to share a secret because the sender does not trust the receiver completely. Thus, the sender provides one part of the information to the receiver and shares the other part of the information to a third party on whom the sender can rely. The secret can be revealed when the receiver and the third party agree to cooperate. This is the essence of the secret-sharing protocol. 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 quantum secret sharing protocol exploiting a three-qubit W class of state shared between three parties, Alice (Sender), Bob (Mediator), 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 secret-sharing scheme.

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