Building partially entangled states with Grover's amplitude amplification process
arXiv:quant-ph/9810093 · doi:10.1142/S0129183100000407
Abstract
We discuss how to build some partially entangled states of 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.
22 pages, Latex2e, 8 epsf figures. The title is changed and estimation of the number of quantum gates for our method is corrected. Many parts of the article are rewritten and should hopefully be clear