Scalable and deterministic Greenberger-Horne-Zeilinger state generation via graph states-assisted measurements

TL;DR

This paper introduces a scalable, deterministic protocol for generating large, highly entangled multi-qubit states using graph state-assisted measurements, improving entanglement concentration and robustness.

Contribution

It presents a novel protocol that enhances bipartite entanglement in multi-qubit states through graph basis measurements, with proven equivalence to measurement-based methods.

Findings

Achieves higher bipartite entanglement than initial pairs.

Demonstrates realization via two-qubit parity measurements.

Establishes bounds on entanglement concentration after multiple rounds.

Abstract

We propose a scalable and deterministic protocol for growing large multi-qubit states starting from two-qubit non-maximally entangled pure states, where the bipartite entanglement in the resultant state is higher than the maximum of the available entangled qubit-pairs. This is achieved via a truncation of the Hilbert space corresponding to a subsystem of qubits to a space that hosts a single qubit, brought about by a multi-qubit measurement assisted by the graph basis. We prove its equivalence to a repetitive two-qubit measurement-based protocol, and demonstrate realization of the required two-qubit measurement via a two-qubit parity measurement, thereby establishing the implementability of the protocol. We derive lower and upper bounds of the bipartite entanglement concentrated after a given number of rounds of measurements, where the entanglement of the available qubit-pairs are not-necessarily equal. We further discuss the effect of possible imperfections that may arise in the protocol, and its robustness towards such imperfections. We demonstrate the usefulness of our proposal by applying it to create generalized GHZ states on arbitrary number of qubits, thereby underlining the possibility of creating maximally entangled qubit pairs via qubit-local projection measurements.