What should we add?

Currently, the Qiskit Statevector class does not provide a built-in method to easily check if a quantum state is entangled or separable. I have searched extensively for existing implementations or methods within the library and other resources but could not find a straightforward solution.

To address this gap, I've developed a simple yet efficient method, is_entangled, to determine if a given statevector represents an entangled state using the Von Neumann entropy criterion. The method evaluates single-qubit subsystems, and if any subsystem exhibits entropy greater than a specified threshold (epsilon), the state is classified as entangled.

from qiskit.quantum_info import Statevector, DensityMatrix, partial_trace, entropy

def is_entangled(state: Statevector, epsilon: float = 1e-10) -> bool:
    num_qubits = state.num_qubits
    density_matrix = DensityMatrix(state)

    for qubit in range(num_qubits):
        trace_out = [i for i in range(num_qubits) if i != qubit]
        reduced_dm = partial_trace(density_matrix, trace_out)

        subsystem_entropy = entropy(reduced_dm)

        if subsystem_entropy > epsilon:
            return True

    return False

I propose integrating this method directly into the Statevector class or as a utility within qiskit.quantum_info to enhance user experience and simplify entanglement analysis.