Geometric measure of entanglement of quantum graph states prepared with controlled phase shift operators

Abstract

We consider graph states generated by the action of controlled phase shift operators on a separable state of a multi-qubit system. The case when all the qubits are initially prepared in arbitrary states is investigated. We obtain the geometric measure of entanglement of a qubit with the remaining system in graph states represented by arbitrary weighted graphs and establish its relationship with state parameters. For two-qubit graph states, the geometric measure of entanglement is also quantified on IBM's simulator Qiskit Aer and quantum processor ibmq lima based on auxiliary mean spin measurements. The results of quantum computations verify our analytical predictions.