Posner qubits: spin dynamics of entangled Ca9(PO4)6 molecules and their role in neural processing.

It has been suggested that 31P nuclear spins in Ca9(PO4)6 molecules could form the basis of a quantum mechanism for neural processing in the brain. A fundamental requirement of this proposal is that spins in different Ca9(PO4)6 molecules can become entangled and remain so for periods (estimated at many hours) that hugely exceed typical 31P spin relaxation times. Here, we consider the coherent and incoherent spin dynamics of Ca9(PO4)6 arising from dipolar and scalar spin-spin interactions and derive an upper bound of 37 min on the entanglement lifetime under idealized physiological conditions. We argue that the spin relaxation in Ca9(PO4)6 is likely to be much faster than this estimate.