Reducible Correlations in Dicke States

TL;DR

This paper demonstrates that generalized Dicke states' correlations can be fully characterized from their reduced subsystems, simplifying analysis by focusing on diagonal elements and reducing the problem to a smaller subsystem size.

Contribution

It introduces a method to determine generalized Dicke states from reduced density matrices, reducing the correlation analysis to a 2ℓ-partite level, with implications for the Quantum Marginal Problem.

Findings

Correlation in generalized Dicke states reduces to 2ℓ-partite level.

Diagonal elements of reduced density matrices suffice for state determination.

Application to the Quantum Marginal Problem discussed.

Abstract

We apply a simple observation to show that the generalized Dicke states can be determined from their reduced subsystems. In this framework, it is sufficient to calculate the expression for only the diagonal elements of the reudced density matrices in terms of the state coefficients. We prove that the correlation in generalized Dicke states $|GD_N^{(\ell)}>$ can be reduced to $2\ell$-partite level. Application to the Quantum Marginal Problem is also discussed.