Towards the State Space Interpretation (SSI): A Formalized Framework for Game Studies and Design

In this paper, we establish structural analogies between core concepts in quantum mechanics and games. By constructing the Quantum Coin Toss on a quantum circuit, we preliminarily investigate the similarity between quantum system behavior and game behavior, thereby formulating the state-operation paradigm. Using this paradigm, we introduce the conceptual prototype of the State Space Interpretation (SSI). Based on mathematical and physical theories, particularly linear algebra, quantum mechanics, and statistical mechanics, we define formal constructs including state space, evolution path, and derived concepts. With the SSI, a game is conceptualized as a state space, while a gameplay process corresponds to an evolution path within this space. We propose that the SSI constitutes a novel interpretation framework for game design and game studies. This framework aims to enhance understanding of games and function as a link between game studies and related fields.