Expanding a 4-qubit Dicke state to a 5-qubit Dicke state with limited qubit access

Abstract

Preparing multipartite entangled states under restricted qubit access is a key challenge for modular and distributed quantum architectures. We address this by presenting two complementary circuits. First, we propose a resource-efficient deterministic circuit for preparing the four-qubit Dicke state with two excitations, requiring only six two-qubit controlled gates, which is fewer than previously reported schemes. Second, we introduce a probabilistic expansion protocol that transforms a four-qubit Dicke state with two excitations into a five-qubit Dicke state with three excitations, even when only a subset of qubits is accessible and one qubit remains untouched. The expansion succeeds with a probability of 5/6; in the remaining 1/6 of cases, the post-measurement state is a recyclable three-qubit W-like state that can be used to regenerate the initial four-qubit Dicke state. We provide an analytical derivation of the success bound, explicit circuit constructions, and numerical simulations over 105\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^5$$\end{document} runs that confirm the predicted statistics. A robustness analysis using a coherent over-rotation error model applied uniformly to all controlled gates shows that the output fidelity remains high for experimentally relevant deviations, indicating resilience to realistic imperfections. By operating without global access to every qubit, the proposed methods advance Dicke-state generation in settings where direct control is limited and offer practical building blocks for scalable state growth in near-term quantum processors.