Constructing Multipartite Planar Maximally Entangled States from Phase States and Quantum Secret Sharing Protocol

• URL: http://arxiv.org/abs/2411.15077v1
• Date: Fri, 22 Nov 2024 17:10:58 GMT
• Title: Constructing Multipartite Planar Maximally Entangled States from Phase States and Quantum Secret Sharing Protocol
• Authors: Lahoucine Bouhouch, Yassine Dakir, Abdallah Slaoui, Rachid Ahl Laamara,
• Abstract summary: We explore the construction of Planar Maximallyangled (PME) states from phase states. PME states form a class of $n$-partite states in which any subset of adjacent particles whose size is less than or equal to half the total number of particles is in a fully entangled state.
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• Abstract: In this paper, we explore the construction of Planar Maximally Entangled (PME) states from phase states. PME states form a class of $n$-partite states in which any subset of adjacent particles whose size is less than or equal to half the total number of particles is in a fully entangled state. This property is essential to ensuring the robustness and stability of PME states in various quantum information applications. We introduce phase states for a set of so-called noninteracting $n$ particles and describe their corresponding separable density matrices. These phase states, although individually separable, serve as a starting point for the generation of entangled states when subjected to unitary dynamics. Using this method, we suggest a way to make complex multi-qubit states by watching how unconnected phase states change over time with a certain unitary interaction operator. In addition, we show how to derive PME states from these intricate phase states for two-, three-, four-, and K-qubit systems. This method of constructing PME states is particularly relevant for applications in fields such as quantum teleportation, quantum secret sharing, and quantum error correction, where multiparty entanglement plays a central role in the efficiency of the protocols.

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