Generation of entanglement between qubits in a one-dimensional harmonic oscillator

Abstract

We present a scheme for generating entanglement between two qubits associated with a pair of particles, which move and interact, in a one-dimensional harmonic-oscillator potential. The spatial wave functions of the particles are initially localized on either side of the oscillator. As they ``fall'' toward each other, we find that the interaction between the two particles produces an effective exchange interaction between the qubits. This allows us to produce a ``power-of-swap'' operation on the initial two-qubit quantum state without requiring any time-dependent control. We find that under certain conditions, we can generate maximally entangled states from a product state with a fidelity that is only weakly dependent on initialization errors.