Entanglement and coherence in pure and doped Posner molecules*

It has been more than two decades since Bruce Kane proposed that spin-half phosphorus nuclei embedded in a spin-zero silicon substrate might act as a possible implementation of spin quantum computing. The coherence times of isolated nuclear spins are very long, which makes them ideal qubits. In addition to this their sensitivity to magnetic fields allows a measurable means of qubit manipulation. Despite this, spin quantum computing remains an elusive goal. More recently, physicist Matthew Fisher has suggested a role for nuclear spin dynamics in cognition and possibly consciousness. Intriguingly this model involves phosphorus nuclear spin in the spin-zero substrate of calcium phosphate molecules. While the hypothesis has generated a great deal of interest there are integral questions that remain to be answered. We have modelled the spin dynamics of entangled phosphorus nuclei in pure and doped calcium phosphate molecules. Our results suggest a way in which entanglement might be preserved by the presence of the weak geomagnetic field. This result may potentially inform approaches to spin quantum computing. On the other hand, one of the open questions in Fisher's model is how entanglement effects might translate into biological signalling. We investigate how quantum computing models of spin transfer from nuclei to electrons might offer insights into the similar case of spin quantum cognition.