Dicke states as matrix product states

Abstract

We derive an exact canonical matrix product state (MPS) representation for Dicke states $|D_k^n⟩$ with minimal bond dimension $\chi =k+1$, for general values of $n$ and $k$, for which the W-state is the simplest case $k=1$. We use this MPS to formulate a quantum circuit for sequentially preparing Dicke states deterministically, relating it to the recursive algorithm of Bärtschi and Eidenbenz. We also find exact canonical MPS representations with minimal bond dimension for higher-spin and qudit Dicke states.

16 pages + Supplementary Material (cirq code); v2: improvements in the presentation, version to appear in Phys. Rev. A

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Cited by in corpus (6)

• Efficient preparation of Dicke states
• Dicke subsystems are entangled
• Simple ways of preparing qudit Dicke states
• Emergence of global receptive fields capturing multipartite quantum correlations
• Spin-$s$ $U(1)$-eigenstate preparation
• Entanglement in the symmetric subspace: mapping multipartite to bipartite states