We propose a measure to quantify strength of semantic relation between two pairs of binary alternatives in cognition of a subject group. The measure and experimental methodology, adapted from physical toolbox for detection of quantum entanglement, allow for on-line realization when a WWW search engine functions as a model of collective cognition of its users. We demonstrate the method by quantifying culture-specific semantic relations between the archetypal living creatures and their qualities, which previously could be addressed only verbally. Methodology and state-of-the art in quantum approach to semantic modeling of human behavior are outlined.