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Cambridge University Press eBooks

Neurophysiological sources of quantum-like processing in the brain

Emmanuel E. Haven, Andrei Yu. Khrennikov

Published Jan 17, 2013• 0 citations
Publisher

Abstract

Introduction In previous chapters, we discussed the conjecture of quantum-like (QL) processing of information in the brain. See, for instance, Chapter 1 (Section 1.16) and Chapter 3 (Section 3.1). In general, such processing need not be based on the physical quantum brain (see, for instance, Hameroff [1] [2] and Penrose [3] [4]), which is the quantum physical carrier of information. As we remarked in Khrennikov [5], the brain created the QL representation (QLR) of information in Hilbert space. Such representation uses quantum information rules in decision making. The existence of such QLR was (at least preliminary) confirmed by experimental data from cognitive psychology (please see Chapter 8). The violation of the law of total probability in these experiments is an important sign of the non-classicality of data. In the constructive wave function approach (see Section 8.16 of Chapter 8), such data can be represented by complex amplitudes. We also presented the QL model of decision making in Chapter 9. In this chapter we reproduce (with only slight modifications) the paper by Khrennikov [6]. The next natural step is to try to find possible physical realizations of the QLR in the brain. One of the possibilities is to appeal to the quantum physics of the microprocesses in the brain - the quantum brain. However, quite surprisingly, it is possible to proceed within the classical field framework, i.e. to create a classical wave model producing the QLR.

DOI
10.1017/cbo9781139003261.017

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Introduction In previous chapters, we discussed the conjecture of quantum-like (QL) processing of information in the brain. See, for instance, Chapter 1 (Section 1.16) and Chapter 3 (Section 3.1). In general, such processing need not be based on the physical quantum brain (see, for instance, Hameroff [1] [2] and Penrose [3] [4]), which is the quantum physical carrier of information. As we remarked in Khrennikov [5], the brain created the QL representation (QLR) of information in Hilbert space. Such representation uses quantum information rules in decision making. The existence of such QLR was (at least preliminary) confirmed by experimental data from cognitive psychology (please see Chapter 8). The violation of the law of total probability in these experiments is an important sign of the non-classicality of data. In the constructive wave function approach (see Section 8.16 of Chapter 8), such data can be represented by complex amplitudes. We also presented the QL model of decision making in Chapter 9. In this chapter we reproduce (with only slight modifications) the paper by Khrennikov [6]. The next natural step is to try to find possible physical realizations of the QLR in the brain. One of the possibilities is to appeal to the quantum physics of the microprocesses in the brain - the quantum brain. However, quite surprisingly, it is possible to proceed within the classical field framework, i.e. to create a classical wave model producing the QLR.
We discuss the conjecture on quantum-like (QL) processing of information in the brain. It is not based on the physical quantum brain (e.g., Penrose) - quantum physical carriers of information. In our approach the brain created the QL representation (QLR) of information in Hilbert space. It uses quantum information rules in decision making. The existence of such QLR was (at least preliminary) confirmed by experimental data from cognitive psychology; in particular, experiments on recognition of ambiguous figures (Conte et al., 2006; 2009). The violation of the law of total probability in these experiments is an important sign of nonclassicality of data. In this paper we speculate on a possible physical realization of QLR in the brain: a classical wave model producing QLR . It is based on variety of time scales in the brain. Each pair of scales (fine - the background fluctuations of electromagnetic field and rough - the cognitive image scale) induces the QL representation. The background field plays the crucial role in creation of “superstrong QL correlations” in the brain.
Introduction In the previous chapter, we presented experimental data from cognitive psychology which can be considered as a strong argument in favor of the complex (or more general) Hilbert space representation of information by cognitive systems and the use of the quantum information scheme in information processing. We have seen that the classical Law of Total Probability (LTP) is violated. The interference of probabilities induces a possibility to “reconstruct a mental wave function.” An important lesson we can learn from this is that the standard Dirac-von Neumann approach based on self-adjoint operators is too restrictive to describe known data from cognitive psychology. More general quantum models should be used. Please see also Appendix 2, this chapter. In this chapter, we proceed under the assumption (which we consider as sufficiently confirmed experimentally) that in order to make decisions, cognitive systems operate with “mental wave functions.” We describe the scheme of such decision making based on the lifting formalism, see Appendix 1, this chapter. Since this book is oriented towards non-experts in quantum information theory, we try to avoid the use of the lifting concept as long as is tolerable. In principle, the reader can proceed without using the lifting concept. However, the formulation in terms of lifting is mathematically elegant and it provides a possibility for further generalizations of the model.
We present the quantum-like model of information processing by the brain’s neural networks. The model does not refer to genuine quantum processes in the brain. In this model, uncertainty generated by the action potential of a neuron is represented as quantum-like superposition of the basic mental states corresponding to a neural code. Neuron’s state space is described as complex Hilbert space (quantum information representation). The brain’s psychological functions perform self-measurements by extracting concrete answers to questions (solutions of problems) from quantum information states. This extraction is modeled in the framework of open quantum systems theory. In this way, it is possible to proceed without appealing to the state’s collapse. Dynamics of the state of psychological function F is described by the quantum master equation. Its stationary states represent classical statistical mixtures of possible outputs of F (decisions). This model can be used for justification of quantum-like modeling cognition and decision-making. The latter is supported by plenty of statistical data collected in cognitive psychology.
Quantum-like modeling (QLM) – quantum theory applications outside of physics – are intensively developed with applications in biology, cognition, psychology, and decision-making. For cognition, QLM should be distinguished from quantum reductionist models in the spirit of Hameroff and Penrose and well as Umezawa and Vitiello. QLM is not concerned with just quantum physical processes in the brain but also QL information processing by macroscopic neuronal structures. Although QLM of cognition and decision-making has seen some success, it suffers from a knowledge gap that exists between oscillatory neuronal network functioning in the brain and QL behavioral patterns. Recently, steps toward closing this gap have been taken using the generalized probability theory and prequantum classical statistical field theory (PCSFT) – a random field model beyond the complex Hilbert space formalism. PCSFT is used to move from the classical ``oscillatory cognition'' of the neuronal networks to QLM for decision-making. In this study, we addressed the most difficult problem within this construction: QLM for entanglement generation by classical networks, i.e., “mental entanglement.” We started with the observational approach to entanglement based on operator algebras describing “local observables” and bringing into being the tensor product structure in the space of QL states. Moreover, we applied the standard states entanglement approach: entanglement generation by spatially separated networks in the brain. Finally, we discussed possible future experiments on “mental entanglement” detection using the EEG/MEG technique.
Quantum-like modeling (QLM)– quantum theory applications outside of physics– are intensively developed with applications in biology, cognition, psychology, and decision-making. For cognition, QLM should be distinguished from quantum reductionist models in the spirit of Hameroff and Penrose and well as Umezawa and Vitiello. QLM is not concerned with just quantum physical processes in the brain but also QL information processing by macroscopic neuronal structures. Although QLM of cognition and decision-making has seen some success, it suffers from a knowledge gap that exists between oscillatory neuronal network functioning in the brain and QL behavioral patterns. Recently, steps toward closing this gap have been taken using the generalized probability theory and prequantum classical statistical field theory (PCSFT)– a random field model beyond the complex Hilbert space formalism. PCSFT is used to move from the classical “oscillatory cognition” of the neuronal networks to QLM for decision-making. In this study, we addressed the most difficult problem within this construction: QLM for entanglement generation by classical networks, i.e., “mental entanglement”. We started with the observational approach to entanglement based on operator algebras describing “local observables” and bringing into being the tensor product structure in the space of QL states. Moreover, we applied the standard states entanglement approach: entanglement generation by spatially separated networks in the brain. Finally, we discussed possible future experiments on “mental entanglement” detection using the EEG/MEG technique.
Quantum-like modeling (QLM) – quantum theory applications outside of physics – are intensively developed with applications in biology, cognition, psychology, and decision-making. For cognition, QLM should be distinguished from quantum reductionist models in the spirit of Hameroff and Penrose and well as Umezawa and Vitiello. QLM is not concerned with just quantum physical processes in the brain but also QL information processing by macroscopic neuronal structures. Although QLM of cognition and decision-making has seen some success, it suffers from a knowledge gap that exists between oscillatory neuronal network functioning in the brain and QL behavioral patterns. Recently, steps toward closing this gap have been taken using the generalized probability theory and prequantum classical statistical field theory (PCSFT) – a random field model beyond the complex Hilbert space formalism. PCSFT is used to move from the classical ``oscillatory cognition'' of the neuronal networks to QLM for decision-making. In this study, we addressed the most difficult problem within this construction: QLM for entanglement generation by classical networks, i.e., “mental entanglement.” We started with the observational approach to entanglement based on operator algebras describing “local observables” and bringing into being the tensor product structure in the space of QL states. Moreover, we applied the standard states entanglement approach: entanglement generation by spatially separated networks in the brain. Finally, we discussed possible future experiments on “mental entanglement” detection using the EEG/MEG technique.