Building partially entangled states with Grover's amplitude amplification process

We discuss how to build some partially entangled states of $n$ two-state quantum systems (qubits). The optimal partially entangled state with a high degree of symmetry is considered to be useful for overcoming a shot noise limit of Ramsey spectroscopy under some decoherence. This state is invariant under permutation of any two qubits and inversion between the ground state |0\ket and an excited state |1\ket for each qubit. We show that using selective phase shifts in certain basis vectors and Grover's inversion about average operations, we can construct this high symmetric entangled state by ({polynomial in n})\times 2^{n/2} successive unitary transformations that are applied on two or three qubits. We can apply our method to build more general entangled states.