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Quantum Secret Sharing using GHZ State Qubit Positioning and Selective Qubits Strategy with Simulation Analysis

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Abstract

This paper presents a novel (3, 3) quantum secret sharing scheme using GHZ product state. Using the classical information to be shared, a dealer toggles the qubits, and then shares the product state. The other three parties make their Bell measurements and collude to reconstruct the secret. Unlike the other existing protocols, the proposed protocol does not involve the entire initial state in the secret reconstruction and discard the redundant qubits at the time of reconstruction to decode the secret. The protocol also allows for security against malicious attacks by an adversary without affecting the integrity of the secret. The security of the protocol lies in the fact that each party’s correct announcement of their measurement is required for reconstruction, failing which the reconstruction process is jeopardized, thereby ascertaining the (3, 3) scheme which has the potential to be generalized to a (t, t) protocol in a similar way. The simulation of the protocol has been performed on IBM-QE platform with backend providers IBMQ_16_Melbourne, IBMQ_Casablanca and IBMQ_Qasm_simulator_V0.1.547.

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Acknowledgements

One of the authors, Farhan Musanna, is grateful to the Ministry of Human Resource Development, India and the Indian Institute of Technology, Roorkee for being the funding agency of this work. The grant number is MHR-01-23-200-428. The work is also partially funded by the project grant no. CRG/2020/002040 of SERB New Delhi, India. The authors are extremely thankful to IBM for providing access to their Quantum Experience (IBM-QE) cloud servers.

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  1. School of Mathematics, Thapar Institute of Engineering & Technology, Patiala, Punjab, India

    Farhan Musanna

  2. Department of Mathematics, IIT Roorkee, Roorkee, India

    Sanjeev Kumar

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  1. Farhan Musanna
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  2. Sanjeev Kumar
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Correspondence to Farhan Musanna.

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Musanna, F., Kumar, S. Quantum Secret Sharing using GHZ State Qubit Positioning and Selective Qubits Strategy with Simulation Analysis. Int J Theor Phys 61, 255 (2022). https://doi.org/10.1007/s10773-022-05237-0

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