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

Radical-pair reactions pertinent to biological magnetic field sensing are an ideal system for demonstrating the paradigm of quantum biology, the exploration of quantum coherence effects in complex biological systems. We here provide yet another fundamental connection between this biochemical spin system and quantum information science. We introduce and explore a formal measure quantifying the singlet-triplet coherence of radical pairs using the concept of quantum relative entropy. The ability to quantify singlet-triplet coherence opens up a number of possibilities in the study of magnetic sensing with radical pairs. We first use the explicit quantification of singlet-triplet coherence to affirmatively address the major premise of quantum biology, namely, that quantum coherence provides an operational advantage to magnetoreception. Second, we use the concept of incoherent operations to show that incoherent manipulations of nuclear spins can have a dire effect on singlet-triplet coherence when the radical pair exhibits electronic-nuclear entanglement. Finally, we unravel subtle effects related to exchange interactions and their role in promoting quantum coherence.