# Monogamous nature of symmetric multiqubt states with distinct spinors

## TL;DR

This paper investigates monogamy relations in symmetric multiqubit states with two distinct spinors, revealing that states with equal spinor distribution exhibit stronger monogamy and higher residual entanglement.

## Contribution

It introduces a detailed analysis of monogamy relations in generalized Dicke states using Majorana representation and identifies conditions for maximal residual entanglement.

## Key findings

- States with equal spinor distribution are more monogamous.
- Residual entanglement is larger in states with equal spinor distribution.
- Boundaries of monogamy inequality are characterized for these states.

## Abstract

Monogamy relations place restrictions on the shareability of quantum corellations in multipartite states. Being an intrinsic quantum feature, monogamy property throws light on {\emph{residual}} entanglement, an entanglement which is not accounted for by the pairwise entanglement in the state. Expressed in terms of suitable pairwise entanglement measures such as concurrence, the monogamy inequality leads to the evaluation of {\emph{tangle}}, a measure of residual entanglement. In this work, we explore monogamy relations in pure symmetric multiqubit states constituted by two distinct spinors, the so-called {\emph{Dicke-class}} of states. Pure symmetric $N$-qubit states constituted by permutation of two orthogonal qubits form the well-known Dicke states. Those $N$-qubit pure symmetric states constructed by permutations of two non-orthogonal qubits are a one-parameter class of generalized Dicke states. With the help of Majorana geometric representation and angular momentum algebra, we analyze the bounds on monogamy inequality, expressed in terms of squared concurrence/squared negativity of partial transpose. We show that the states with equal distribution of the two spinors are more monogamous and hence possess larger residual entanglement when compared to other inequivalent classes with different degeneracy configurations.