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What is the real role of the quantum coherence and entanglement in theradical pair (RP) compass, and what determines the singlet yield have not beenfully understood. In this paper, we find that the dark states of thetwo-electron Zeeman energy operator (TEZE) play an important role in the RPcompass. We respectively calculate the singlet yields for two initial states inthis dark state basis: the coherent state and the same state just removing thedark state coherence. For the later there is neither dark state coherence norentanglement in the whole dynamical process. Surprisingly we find that in bothcases the singlet yields are the same, and based on this result, we believethat the dark state population determines the singlet yield completely, and thedark state coherence and entanglement have little contribution to it. Finally,we also find that the dark state population as well as the singlet yieldanisotropy is fragile to the vertical magnetic noise. However, the orientationis robust and is even enhanced by the parallel magnetic noise because the darkstates expand a decoherence-free subspace. The dark state population as well asthe orientation is more robust to the hyperfine coupling noise.

Dark state population determines magnetic sensitivity in radical pair magnetoreception model