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The Nth Roots of Any Complex Number z = e^iφ Are Given by z_k=e^iφk Where φ_k=(φ+2kπ/N), k = 0,1,2,...,N-1.

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• TITLE: Entanglement and Volume Monogamy Features of Permutation Symmetric N-Qubit Pure States with N-Distinct Spinors: GHZ and States

  AUTHORS: Sudha, Alevoor Raghavendra Usha Devi, Akshata Shenoy Hejamadi, Hosapete Seshadri Karthik, Humera Talath, Bada Palaiah Govindaraja, Attipat Krishnaswamy Rajagopal

  KEYWORDS: Permutation Symmetric States, Monogamy, Pairwise Entanglement

  JOURNAL NAME: Journal of Quantum Information Science, Vol.14 No.2, April 7, 2024

  ABSTRACT: We explore the entanglement features of pure symmetric N-qubit states characterized by N-distinct spinors with a particular focus on the Greenberger-Horne-Zeilinger (GHZ) states and , an equal superposition of W and obverse W states. Along with a comparison of pairwise entanglement and monogamy properties, we explore the geometric information contained in them by constructing their canonical steering ellipsoids. We obtain the volume monogamy relations satisfied by states as a function of number of qubits and compare with the maximal monogamy property of GHZ states.