Expanding a 4-qubit Dicke State to a 5-qubit Dicke State with Limited Qubit Access

TL;DR

This paper introduces a method to expand a four-qubit Dicke state into a five-qubit Dicke state using limited qubit access, supported by a specialized quantum circuit and robustness analysis under noise.

Contribution

It presents a novel quantum circuit for expanding Dicke states with restricted qubit control, including analytical derivation and numerical simulation validation.

Findings

The circuit successfully expands Dicke states with high fidelity.

The method is robust against common experimental errors.

Numerical simulations confirm practical feasibility.

Abstract

In scenarios where full access to all qubits of a multipartite quantum system is available and global operations can be implemented, the preparation of arbitrary entangled states is theoretically straightforward. However, practical constraints often limit direct control over all qubits. In this work, we first present an efficient method for preparing a four-qubit Dicke state, and then demonstrate how a four-qubit Dicke state can be expanded to a five-qubit Dicke state even when only a subset of qubits is accessible. We propose a quantum circuit that achieves this transformation under restricted control, and support our analytical derivation with numerical simulations. We further carry out a robustness analysis of our circuit under imperfect gate implementations and find that it retains high fidelity for experimentally relevant levels of coherent over-rotation errors, confirming its resilience to realistic noise.