Symmetric multiqudit states: Stars, entanglement, and rotosensors

A constellation of $N=d-1$ Majorana stars represents an arbitrary pure quantum state dimension $d$ or a permutation-symmetric system consisting $n$ qubits. We generalize the latter construction to represent in similar way symmetric $k$ subsystems with levels each. For $d\geq 3$, such states are equivalent, as far rotations concerned, collection various spin states, definite relative complex weights. Following Majorana's lead, we introduce multiconstellation, constellations above augmented by auxiliary, "spectator" constellation, encoding Examples stellar representations four qutrits, and two spin-$3/2$ systems, presented. revisit Hermite Murnaghan isomorphisms, which relate multipartite spins, number parties, even symmetries. show how tools introduced can be used analyze entanglement identify optimal rotosensors, i.e., maximally sensitive around specified axis, averaged over all axes.