Figure 2

Compass sensitivity, as captured by the anisotropy \(\Delta _{S}\), is plotted against electronic coherence measures \(\mu [\bar{{\mathcal {C}}}_{i}]\) (a, c, e) and \(\Delta [\bar{{\mathcal {C}}}_{i}]\) (b, d, f), for 878,400 relative orientations of flavin–tryptophan radical pairs. The anisotropy \(\Delta _{S}\) quantifies the maximal change in the recombination quantum yield as the direction of the applied magnetic field is varied in the frame of the cryptochrome protein, with larger values corresponding to greater sensitivity. Here, we use the recombination weighted relative entropy of coherence \(\bar{{\mathcal {C}}}_{r}\) defined in Eq. (4), and the \(l_{1}\)-norm measure \(\bar{{\mathcal {C}}}_{l_{1}}\) defined in Eq. (5) evaluated in the Zeeman basis, also known as the “up-down” (UD) basis, and the singlet-triplet (ST) basis. Coherence is assessed by its mean value \(\mu [\bar{{\mathcal {C}}}_{i}]\) as defined in Eq. (8), and difference \(\Delta [\bar{{\mathcal {C}}}_{i}]\) as defined in Eq. (9), with respect to the magnetic field directions associated with maximal and minimal recombination yield. Alternative measures are covered in the Supporting Information. Data has been coloured according to the relative orientation angle \(\beta\), ranging from 0° (blue) to 180° (yellow) and a linear fit (red line) with associated Pearson correlation coefficient R is displayed.