Dicke subsystems are entangled

Abstract

We show that all reduced states of nonproduct symmetric Dicke states of arbitrary number of qudits are genuinely multipartite entangled, and of nonpositive partial transpose with respect to any subsystem.

Figures (1)

• Figure 1: Example of the index sets $I^d_n$\ref{['eq:indexset']} and $I^d_{m,{\boldsymbol{n}}}$\ref{['eq:indexset_restr']} for $n=10$ qubits ($d=2$), of occupation ${\boldsymbol{n}}=(7,3)$ for subsystem size $m=6$. Arrows illustrate the occupation number multiindices ${\boldsymbol{m}}$ and ${\boldsymbol{n}}-{\boldsymbol{m}}$, appearing in the decompositions \ref{['eq:Schmidt_nonnorm']} and \ref{['eq:Schmidt_norm']}, adding up to ${\boldsymbol{n}}$.