Entropy Cones and Entanglement Evolution for Dicke States

2023/06/22 by Munizzi, William, Schnitzer, Howard J. · 2 citations
#FOS: Mathematics #FOS: Physical sciences #Group Theory (math.GR) #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2306.13146

Abstract

The N-qubit Dicke states |D^N_k⟩, 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⟩ entropy cone. We demonstrate that all |D^N_k⟩ entropy vectors emerge symmetrized, and use this to define a min-cut protocol on star graphs which realizes |D^N_k⟩ entropy vectors. We identify the stabilizer group for all |D^N_k⟩, under the action of the N-qubit Pauli group and two-qubit Clifford group, which we use to construct |D^N_k⟩ reachability graphs. We use these reachability graphs to analyze and bound the evolution of |D^N_k⟩ entropy vectors in Clifford circuits.

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• Topological Preparation of Non-Stabilizer States and Clifford Evolution in SU(2)₁ Chern-Simons Theory
• A Compact Framework for Analyzing Asynchronous Entanglement Distribution in Quantum Networks

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