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==10. Connecting electrochemical processes in neural networks with quantum informational processing== | ==10. Connecting electrochemical processes in neural networks with quantum informational processing== | ||
As was emphasized in introduction, quantum-like models are formal operational models describing information processing in biosystems. (in contrast to studies in quantum biology — the science about the genuine quantum physical processes in biosystems). Nevertheless, it is interesting to connect the structure quantum information processing in a biosystem with physical and chemical processes in it. This is a problem of high complexity. Paper (Khrennikov et al., 2018) presents an attempt to proceed in this direction for the human brain — the most complicated biosystem (and at the same time the most interesting for scientists). In the framework of quantum information theory, there was modeled information processing by brain’s neural networks. The quantum information formalization of the states of neural networks is coupled with the electrochemical processes in the brain. The key-point is representation of uncertainty generated by the action potential of a neuron as quantum(-like) superposition of the basic mental states corresponding to a neural code, see Fig. 1 for illustration. | As was emphasized in introduction, quantum-like models are formal operational models describing information processing in biosystems. (in contrast to studies in quantum biology — the science about the genuine quantum physical processes in biosystems). Nevertheless, it is interesting to connect the structure quantum information processing in a biosystem with physical and chemical processes in it. This is a problem of high complexity. Paper (Khrennikov et al., 2018)<ref>Khrennikov A., Basieva I., PothosE.M., Yamato I. | ||
Quantum Probability in Decision Making from Quantum Information Representation of Neuronal States, Sci. Rep., 8 (2018), Article 16225</ref> presents an attempt to proceed in this direction for the human brain — the most complicated biosystem (and at the same time the most interesting for scientists). In the framework of quantum information theory, there was modeled information processing by brain’s neural networks. The quantum information formalization of the states of neural networks is coupled with the electrochemical processes in the brain. The key-point is representation of uncertainty generated by the action potential of a neuron as quantum(-like) superposition of the basic mental states corresponding to a neural code, see Fig. 1 for illustration. | |||
Consider information processing by a single neuron; this is the system <math>S</math> (see Section 8.2). Its quantum information state corresponding to the neural code ''quiescent and firing,'' <math>0/1</math>, can be represented in the two dimensional complex <math>{\mathcal{H}}_{neuron}</math> Hilbert space (qubit space). At a concrete instant of time neuron’s state can be mathematically described by superposition of two states, labeled by <math>|0\rangle</math>,<math>|1\rangle</math>: <math>|\psi_{neuron}\rangle=c_0|0\rangle+c_1|1\rangle</math>. It is assumed that these states are orthogonal and normalized, i.e., <math>\langle0|1\rangle=0</math> and<math>\langle \alpha|\alpha\rangle=1</math>, <math>\alpha=0,1</math>. The coordinates <math>c_0</math> and <math>c_1</math> with respect to the quiescent-firing basis are complex amplitudes representing potentialities for the neuron <math>S</math> to be quiescent or firing. Superposition represents uncertainty in action potential, “to fire” or “not to fire”. This superposition is quantum information representation of physical, electrochemical uncertainty. | Consider information processing by a single neuron; this is the system <math>S</math> (see Section 8.2). Its quantum information state corresponding to the neural code ''quiescent and firing,'' <math>0/1</math>, can be represented in the two dimensional complex <math>{\mathcal{H}}_{neuron}</math> Hilbert space (qubit space). At a concrete instant of time neuron’s state can be mathematically described by superposition of two states, labeled by <math>|0\rangle</math>,<math>|1\rangle</math>: <math>|\psi_{neuron}\rangle=c_0|0\rangle+c_1|1\rangle</math>. It is assumed that these states are orthogonal and normalized, i.e., <math>\langle0|1\rangle=0</math> and<math>\langle \alpha|\alpha\rangle=1</math>, <math>\alpha=0,1</math>. The coordinates <math>c_0</math> and <math>c_1</math> with respect to the quiescent-firing basis are complex amplitudes representing potentialities for the neuron <math>S</math> to be quiescent or firing. Superposition represents uncertainty in action potential, “to fire” or “not to fire”. This superposition is quantum information representation of physical, electrochemical uncertainty. | ||