Quantum-inspired density-matrix recurrence analysis of brain time series

Abstract Recurrence analysis allows the investigation of self-similarities in time series. Different degrees of regularity of behaviours, or different typologies of chaos, help characterise physical phenomena whose properties are expressed by time series. We consider here the special case of time series of human brain activity in the insula, an area particularly relevant for emotional and cognitive processing. Starting from time series obtained using functional magnetic resonance imaging, we adopt recurrence plots to investigate differences between normal and selected pathological behaviours. We also present a technique to encode time series into quantum-inspired states, by constructing a density matrix via a kernel mapping. Recurrence structures are derived from similarities between the components of its principal eigenvector. The obtained results highlight differences in behaviour between the time series. Overall, this conceptual study bridges ideas from nonlinear physics, quantum physics, and medical physics.