Constructions of Dicke states in high spin multi-particle systems

TL;DR

This paper provides explicit constructions of Dicke states for high-spin multi-particle systems, offering complete bases, coefficients, and entanglement analysis for spin-1 cases, advancing understanding of multi-particle quantum states.

Contribution

It introduces explicit constructions of Dicke states for spin-1, 3/2, and 2 systems, including bases, coefficients, and anti-symmetric state rules, with entanglement analysis for spin-1 states.

Findings

Explicit bases and coefficients for Dicke states are derived.

A rule for constructing anti-symmetric states in high-spin systems is provided.

Entanglement properties of spin-1 Dicke states are analyzed using negativity.

Abstract

We study the constructions of Dicke states of identical particles of spin-$1$, $3/2$ and $2$ in the number representation with given particle number $N$ and magnetic quantum number $M$. The complete bases and corresponding coefficients in the Dicke states are given, in terms of which the Dicke states are explicitly expressed in the number representation. As a byproduct, a rule of how to construct all the anti-symmetric states in these high spin systems is given. Finally, by employing the negativity as the entanglement measure, we explore the entanglement properties for spin-$1$ cases including certain pure states of two particles and many-particle Dicke states.