Geometric Measure of Entanglement of Quantum Graph States Prepared with Controlled Phase Shift Operators

We will consider graph states generated by the action of controlled phase shift operators on a separable state of a multiqubit system. The case where all the qubits are initially prepared in arbitrary states is investigated. We will obtain the geometric measure of entanglement of a qubit with the remaining system in graph states represented by arbitrary weighted graphs and will 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 analytic predictions.