Quantum information in the Posner model of quantum cognition

摘要

Matthew Fisher recently postulated a mechanism by which quantum phenomenacould influence cognition: Phosphorus nuclear spins may resist decoherence forlong times. The spins would serve as biological qubits. The qubits may resistdecoherence longer when in Posner molecules. We imagine that Fisher postulatescorrectly. How adroitly could biological systems process quantum information(QI)? We establish a framework for answering. Additionally, we apply biologicalqubits in quantum error correction, quantum communication, and quantumcomputation. First, we posit how the QI encoded by the spins transforms asPosner molecules form. The transformation points to a natural computationalbasis for qubits in Posner molecules. From the basis, we construct a quantumcode that detects arbitrary single-qubit errors. Each molecule encodes onequtrit. Shifting from information storage to computation, we define the modelof Posner quantum computation. To illustrate the model's quantum-communicationability, we show how it can teleport information incoherently: A state'sweights are teleported; the coherences are not. The dephasing results from theentangling operation's simulation of a coarse-grained Bell measurement. WhetherPosner quantum computation is universal remains an open question. However, themodel's operations can efficiently prepare a Posner state usable as a resourcein universal measurement-based quantum computation. The state results fromdeforming the Affleck-Lieb-Kennedy-Tasaki (AKLT) state and is a projectedentangled-pair state (PEPS). Finally, we show that entanglement can affectmolecular-binding rates (by 0.6% in an example). This work opens the door forthe QI-theoretic analysis of biological qubits and Posner molecules.