Quantum-like representation of neuronal networks' activity: modeling “mental entanglement”

<i>Quantum-like modeling</i> (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, as well as Umezawa and Vitiello. QLM is not only concerned with just quantum physical processes in the brain but also with 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 "<i>oscillatory cognition</i>" 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, that is, "<i>mental entanglement</i>." 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.