The Biological Qubit: Calcium Phosphate Dimers, not Trimers

Abstract

The Posner molecule (calcium phosphate trimer), has been hypothesized to function as a biological quantum information processor due to its supposedly long-lived entangled $^{31}$P nuclear spin states. This hypothesis was challenged by our recent finding that the molecule lacks a well-defined rotational axis of symmetry -- an essential assumption in the proposal for Posner-mediated neural processing -- and exists as an asymmetric dynamical ensemble. Following up, we investigate here the spin dynamics of the molecule's entangled $^{31}$P nuclear spins within the asymmetric ensemble. Our simulations show that entanglement between two nuclear spins prepared in a Bell state in separate Posner molecules decays on a sub-second timescale -- much faster than previously hypothesized, and not long enough for super-cellular neuronal processing. Calcium phosphate dimers however, are found to be surprisingly resilient to decoherence and are able to preserve entangled nuclear spins for hundreds of seconds, suggesting that neural processing might occur through them instead.