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Quantum Secret Sharing Protocol Using Maximally Entangled Multi-qudit States

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Abstract

The purpose of this paper is to develop a (N − k) threshold quantum secret sharing (QSS) scheme by using entangled multi-qudit states shared between N qudits such that (k ≤ N − k). We introduce first multi-qudit separable states of a Hilbert space associated with a disconnected multi-qudit system. The entangled multi-qudit states are obtained from disconnected states by means of a unitary interaction operator governing the evolution of the multi-qudit system, where the pairwise interaction establishes links between qudits. The generated entangled states are chosen to be maximally entangled with respect to a specific bi-partition (\(A_{2} \bigcup A_{1} \)) with k = |A2|≤|A1| = (N − k) of the whole system such that the von Neumann entropy \(S(\rho _{A_{2}})\) is maximal. The maximally entanglement property with respect to the splitting (\(A_{2} \bigcup A_{1} \)) of this N-qudit entangled states will be used by a dealer (D) to share an encoded quantum secret with (N − 1) other players, such that at least the (N − k) specified players belonging to A1 have to cooperate jointly to get the complete information about the secret.

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Authors and Affiliations

  1. Department of Physics, Faculty of Sciences Aïn ChockUniversity of Hassan II, Casablanca, Morocco

    M. Mansour

  2. LHEP-Modeling and Simulation, Faculty of Sciences, Mohammed V University, Rabat, Morocco

    Z. Dahbi

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  1. M. Mansour
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  2. Z. Dahbi
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Mansour, M., Dahbi, Z. Quantum Secret Sharing Protocol Using Maximally Entangled Multi-qudit States. Int J Theor Phys 59, 3876–3887 (2020). https://doi.org/10.1007/s10773-020-04639-2

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