According to recent studies in developmental psychology and neuroscience, symbolic language is essentially intersubjective. Empathetically relating to others renders possible the acquisition of linguistic constructs. Intersubjectivity develops in early ontogenetic life when interactions between mother and infant mutually shape their relatedness. Empirical findings suggest that the shared attention and intention involved in those interactions is sustained as it becomes internalized and embodied. Symbolic language is derivative and emerges from shared intentionality. In this paper, we present a formalization of shared intentionality based upon a quantum approach. From a phenomenological viewpoint, we investigate the nonseparable, dynamic and sustainable nature of social cognition and evaluate the appropriateness of quantum interaction for modelling intersubjectivity.