Geometric measure of entanglement of multi-qubit graph states and its detection on a quantum computer

TL;DR

This paper introduces a method to quantify the geometric measure of entanglement in multi-qubit graph states, analyzes its dependence on graph properties, and demonstrates its detection on a quantum computer with results matching theoretical predictions.

Contribution

It provides an analytical framework for measuring entanglement in graph states and experimentally verifies it on a real quantum device.

Findings

Entanglement depends on vertex degree and phase parameters.

Quantum computer measurements agree with analytical calculations.

Method applicable to arbitrary graph states.

Abstract

Multi-qubit graph states generated by the action of controlled phase shift operators on a separable quantum state of a system, in which all the qubits are in arbitrary identical states, are examined. The geometric measure of entanglement of a qubit with other qubits is found for the graph states represented by arbitrary graphs. The entanglement depends on the degree of the vertex representing the qubit, the absolute values of the parameter of the phase shift gate, and the parameter of state the gate is acting on. Also, the geometric measure of entanglement of the graph states is quantified on the quantum computer $\textrm{ibmq\_athens}$. The results obtained on the quantum device are in good agreement with analytical ones.