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The possibility that quantum processing with nuclear spins might be operativein the brain is proposed and then explored. Phosphorus is identified as theunique biological element with a nuclear spin that can serve as a qubit forsuch putative quantum processing - a neural qubit - while the phosphate ion isthe only possible qubit-transporter. We identify the "Posner molecule",$\text{Ca}_9 (\text{PO}_4)_6$, as the unique molecule that can protect theneural qubits on very long times and thereby serve as a (working)quantum-memory. A central requirement for quantum-processing is quantumentanglement. It is argued that the enzyme catalyzed chemical reaction whichbreaks a pyrophosphate ion into two phosphate ions can quantum entangle pairsof qubits. Posner molecules, formed by binding such phosphate pairs withextracellular calcium ions, will inherit the nuclear spin entanglement. Amechanism for transporting Posner molecules into presynaptic neurons during a"kiss and run" exocytosis, which releases neurotransmitters into the synapticcleft, is proposed. Quantum measurements can occur when a pair of Posnermolecules chemically bind and subsequently melt, releasing a shower ofintra-cellular calcium ions that can trigger further neurotransmitter releaseand enhance the probability of post-synaptic neuron firing. Multiple entangledPosner molecules, triggering non-local quantum correlations of neuron firingrates, would provide the key mechanism for neural quantum processing.Implications, both in vitro and in vivo, are briefly mentioned.

Quantum Cognition: The possibility of processing with nuclear spins in the brain