Entropy Cones and Entanglement Evolution for Dicke States

• URL: http://arxiv.org/abs/2306.13146v2
• Date: Thu, 23 Nov 2023 02:05:08 GMT
• Title: Entropy Cones and Entanglement Evolution for Dicke States
• Abstract summary: We present a general calculation of entanglement entropy in Dicke states, which we use to describe the $|DN_krangle$ entropy cone. We identify the stabilizer group for all $|DN_krangle$, under the action of the $N$-qubit Pauli group and two-qubit Clifford group. We use these reachability graphs to analyze and bound the evolution of $|DN_krangle$ entropy vectors in Clifford circuits.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The $N$-qubit Dicke states $|D^N_k\rangle$, 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 $|D^N_k\rangle$ entropy cone. We demonstrate that all $|D^N_k\rangle$ entropy vectors emerge symmetrized, and use this to define a min-cut protocol on star graphs which realizes $|D^N_k\rangle$ entropy vectors. We identify the stabilizer group for all $|D^N_k\rangle$, under the action of the $N$-qubit Pauli group and two-qubit Clifford group, which we use to construct $|D^N_k\rangle$ reachability graphs. We use these reachability graphs to analyze and bound the evolution of $|D^N_k\rangle$ entropy vectors in Clifford circuits.

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