Characterizing the entanglement of symmetric many-particle spin-1/2 systems

Analyzing the properties of entanglement in many-particle spin-1/2 systems is generally difficult because the system's Hilbert space grows exponentially with the number of constituent particles, $N$. Fortunately, it is still possible to investigate many-particle entanglement when the state of the system possesses sufficient symmetry. In this paper, we present a practical method for efficiently computing various bipartite entanglement measures for states in the symmetric subspace and perform these calculations for $N\sim 10^3$. By considering all possible bipartite splits, we construct a picture of the multiscale entanglement in large symmetric systems. In particular, we characterize dynamically generated spin-squeezed states by comparing them to known reference states (e.g., GHZ and Dicke states) and new families of states with near-maximal bipartite entropy. We quantify the trade-off between the degree of entanglement and its robustness to particle loss, emphasizing that substantial entanglement need not be fragile.