Abstract
In the present study, 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> and an excited state |1> for each qubit. We show that by 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) ×2n/2 successive unitary transformations that are applied on two or three qubits.
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