Building partially entangled states with Grover's amplitude amplification process

Details Building partially entangled states with Grover's amplitude amplification process Building partially entangled states with Grover's amplitude amplification process

1998-10-30

arxiv.org/abs/quant-ph/9810093v2

Int.J.Mod.Phys. C11 (2000) 469-484

Physics

Quantum Physics

22 pages, Latex2e, 8 epsf figures. The title is changed and estimation of the number of quantum gates for our method is correc

Scientific paper

10.1142/S0129183100000407

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.

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