Resilience of singlet-state extraction against non-optimal resonance conditions

We have recently presented a protocol for extracting the singlet state of two non-interacting high-dimensional spins through post-selection of the internal state of interaction mediators sent in succession [F. Ciccarello et al., arXiv:0710.3855v1]. The scheme requires each mediator's wavevector to obey appropriate resonance conditions. Here we show the robustness of the scheme in the realistic case where such conditions are not sharply fulfilled.