Decision making is a vital function in this age of machine learning and artificial intelligence, yet its physical realization and theoretical fundamentals are still not completely understood. In our former study, we demonstrated that single-photons can be used to make decisions in uncertain, dynamically changing environments. The two-armed bandit problem was successfully solved using the dual probabilistic and particle attributes of single photons. In this study, we present a category theoretic modeling and analysis of single-photon-based decision making, including a quantitative analysis that is in agreement with the experimental results. A category theoretic model reveals the complex interdependencies of subject matter entities in a simplified manner, even in dynamically changing environments. In particular, the octahedral and braid structures in triangulated categories provide a better understanding and quantitative metrics of the underlying mechanisms of a single-photon decision maker. This study provides both insight and a foundation for analyzing more complex and uncertain problems, to further machine learning and artificial intelligence.
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