Entropy cones and entanglement evolution for Dicke states
William Munizzi, Howard J. Schnitzer · Physical Review A · 2024
The $N$-qubit Dicke states $|{D}_{k}^{N}\ensuremath{\rangle}$, of Hamming weight $k$, are a class of entangled states which play an important role in quantum algorithm optimization. We present a general calculation of entanglement entropy in Dicke states, which we use to describe the $|{D}_{k}^{N}\ensuremath{\rangle}$ entropy cone. We demonstrate that all $|{D}_{k}^{N}\ensuremath{\rangle}$ entropy vectors emerge symmetrized and use this to define a min-cut protocol on star graphs which realizes $|{D}_{k}^{N}\ensuremath{\rangle}$ entropy vectors. We identify the stabilizer group for all $|{D}_{k}^{N}\ensuremath{\rangle}$, under the action of the $N$-qubit Pauli group and two-qubit Clifford group, which we use to construct $|{D}_{k}^{N}\ensuremath{\rangle}$ reachability graphs. We use these reachability graphs to analyze and bound evolution of $|{D}_{k}^{N}\ensuremath{\rangle}$ entropy vectors in Clifford circuits.