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Conditional quantum logic using two atomic qubits

In this paper we propose and analyze a feasible scheme where the detection of a single scattered photon from two trapped atoms or ions performs a conditional unitary operation on two qubits. As examples we consider the preparation of all four Bell states, the reverse operation that is a Bell measurement, and a CNOT gate. We study the effect of atomic motion and multiple scattering, by evaluating Bell inequalities violations, and by calculating the CNOT gate fidelity.