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

Ivan Franko National University of Lviv, Professor Ivan Vakarchuk Department for Theoretical Physics 12 Drahomanov St., Lviv, 79005, Ukraine and SoftServe Inc. - 2d Sadova St., Lviv, 79021, Ukraine

^(a) khrystyna.gnatenko@gmail.com (corresponding author)

Received: 19 June 2021
Accepted: 9 December 2021

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 . The results obtained on the quantum device are in good agreement with analytical ones.