Dicke states as matrix product states

TL;DR

This paper presents an exact matrix product state representation for Dicke states, enabling efficient quantum circuit design for their deterministic preparation and extending to higher-spin and qudit variants.

Contribution

It introduces minimal bond dimension MPS representations for Dicke states and develops a quantum circuit for their sequential deterministic preparation.

Findings

Exact MPS with bond dimension k+1 for Dicke states

Quantum circuit for deterministic state preparation

Extensions to higher-spin and qudit Dicke states

Abstract

We derive an exact canonical matrix product state (MPS) representation for Dicke states $|D^n_k\rangle$ 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 B\"artschi and Eidenbenz. We also find exact canonical MPS representations with minimal bond dimension for higher-spin and qudit Dicke states.