We present a full quantum treatment of a five-level atomic system coupled to two quantum and two classical light fields. The two quantum fields undergo a cross-phase modulation induced by electro-magnetically induced transparency. The performance of this configuration as a two-qubit quantum phase gate for travelling single-photons is examined. A trade-off between the size of the conditional phase shift and the fidelity of the gate is found. Nonetheless, a satisfactory gate performance is still found to be possible in the transient regime, corresponding to a fast gate operation.
@article{arxiv.quant-ph/0507137,
title = {Quantum Phase Gate Operation Based on Nonlinear Optics: Full Quantum Analysis},
author = {C. Ottaviani and S. Rebic and D. Vitali and P. Tombesi},
journal= {arXiv preprint arXiv:quant-ph/0507137},
year = {2007}
}