Generating GHZ state in 2m-qubit spin network

TL;DR

This paper demonstrates how to generate maximally entangled GHZ states in a 2m-qubit spin network using spectral techniques and specific Hamiltonian couplings, with explicit formulas and entanglement measures.

Contribution

It provides an explicit method and formulas for creating GHZ states in large spin networks based on Johnson graphs, advancing quantum entanglement generation techniques.

Findings

Explicit coupling strengths for GHZ state generation

Calculation of entanglement measures for evolved states

Examples for 4-qubit and 6-qubit networks

Abstract

We consider a pure 2m-qubit initial state to evolve under a particular quantum me- chanical spin Hamiltonian, which can be written in terms of the adjacency matrix of the Johnson network J(2m;m). Then, by using some techniques such as spectral dis- tribution and stratification associated with the graphs, employed in [1, 2], a maximally entangled GHZ state is generated between the antipodes of the network. In fact, an explicit formula is given for the suitable coupling strengths of the hamiltonian, so that a maximally entangled state can be generated between antipodes of the network. By using some known multipartite entanglement measures, the amount of the entanglement of the final evolved state is calculated, and finally two examples of four qubit and six qubit states are considered in details.