Spin squeezing in symmetric multiqubit states with two non-orthogonal Majorana spinors

Enhanced precision measurements using entangled many particle states are crucial for their technological applications in quantum information science and metrology. Squeezed spin states are a class of permutation symmetric N particle entangled states, which exhibit reduced quantum fluctuation in their collective spin angular momentum in a certain direction, and they are useful for quantum enhanced metrology. Permutation symmetric states attract attention as they offer significant test grounds for the description of entanglement in multipartite quantum systems, which is crucial for processing complex quantum information tasks. Spin squeezing serves as an experimentally amenable collective criterion of entanglement in symmetric multiqubit systems. In this paper, we explore spin-squeezing behavior in different classes of N-qubit symmetric states consisting of all permutations of two distinct spinors. We employ Majorana geometric representation of multiqubit states obeying exchange symmetry for this purpose. We prove that N qubit symmetric states consisting of two distinct non-orthogonal spinors do exhibit spin squeezing, thus expanding the avenues of their applicability in quantum enhanced sensing tasks.