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Radical-pair reactions pertinent to biological magnetic field sensing are anideal system for demonstrating the paradigm of quantum biology, the explorationof quantum coherene effects in complex biological systems. We here provide yetanother fundamental connection between this biochemical spin system and quantuminformation science. We introduce and explore a formal measure quantifyingsinglet-triplet coherence of radical-pairs using the concept of quantumrelative entropy. The ability to quantify singlet-triplet coherence opens up anumber of possibilities in the study of magnetic sensing with radical-pairs. Wefirst use the explicit quantification of singlet-triplet coherence toaffirmatively address the major premise of quantum biology, namely that quantumcoherence provides an operational advantage to magnetoreception. Secondly, weuse the concept of incoherent operations to show that incoherent manipulationsof nuclear spins can have a dire effect on singlet-triplet coherence when theradical-pair exhibits electronic-nuclear entanglement. Finally, we unravelsubtle effects related to exchange interactions and their role in promotingquantum coherence.

Quantum relative entropy shows singlet-triplet coherence is a resource in the radical-pair mechanism of biological magnetic sensing