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Building partially entangled states with Grover's amplitude amplification process

Hiroo Azuma
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Abstract

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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Hiroo Azuma. 2000-01-12. Building partially entangled states with Grover's amplitude amplification process. https://doi.org/10.1142/s0129183100000407

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