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's states, the reverse operation that is a Bell's measurement, and a controlled-NOT (CNOT) gate. We study the effect of atomic motion and multiple scattering by evaluating Bell's inequalities violations and by calculating the CNOT gate fidelity.