  A fundamental concept of quantum physics, the Wigner Yanase information, is
here used as a measure of quantum coherence in spin-dependent radical-pair
reactions pertaining to biological magnetic sensing. This measure is connected
to the uncertainty of the reaction yields, and further, to the statistics of a
cellular receptor-ligand system used to biochemically convey magnetic-field
changes. Measurable physiological quantities, such as the number of receptors
and fluctuations in ligand concentration, are shown to reflect the introduced
Wigner-Yanase measure of singlet-triplet coherence. We arrive at a
quantum-biological uncertainty relation, connecting the product of a biological
resource and a biological figure of merit with the Wigner-Yanase coherence. Our
approach can serve a general search for quantum-coherent effects within
cellular environments.
