<p>Presented are mathematical and software tools providing the formation and objective quantitative assessment of teamwork skills based on quantum representations. These tools utilize the formal representations of subjects' activities through probability matrices of transitions between the performed elementary operations. Analysis of the subjects' activities is based on comparisons of these matrices for a pattern of actions under study with relevant matrices for patterns of empirical data representing various variants of the subjects' work. When evaluating the teamwork skills, these comparisons are performed according to the "Triangle Scheme", which involves comparing the coordinated actions of the subjects performed in pairs and individually. For this purpose, the quantum spectral analysis is used, which provides effective quantitative comparisons of the hidden periodicities of performing typical elementary operations and their quantities in the spectral metric. The tools for the formation and assessment of teamwork skills are implemented in the form of both a flight simulator with the separation of control channels between pilots and a modified computer game "Sea Battle", which allows to evaluate the dynamics of partners&rsquo; communication and cooperation by analyzing their moves as well as tips transmitted to each other. The presented approach to the formation and assessment of teamwork skills is quite universal and can be used in various applications areas, including the assessment and training of flight crews, operators of complex technical systems, students of various levels and other target groups.</p>