There exist several phenomena (systems) breaking the classical probability laws. Such systems are contextual dependent adaptive systems. In this paper, we present a new mathematical formula to compute the probability in those systems by using the concepts of the adaptive dynamics and quantum information theory -- quantum channels and the lifting. The basic examples of the contextual dependent phenomena can be found in quantum physics. And recently similar examples were found in biological and psychological sciences. Our novel approach is motivated by traditional quantum probability, but it is general enough to describe aforementioned phenomena outside of quantum physics.
Contextuality as a Diagnostic of Translation-Symmetry Breaking in Translation-Invariant 1D Hamiltonians
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（电子科技大学基础与前沿研究院）；Ministry of Education Key Laboratory of Quantum Physics and Photonic Quantum Information (University of Electronic Science and Technology of China)（量子物理与光量子信息教育部重点实验室（电子科技大学））
Generalised contextuality of continuous variable quantum theory can be revealed with a single projective measurement
Uppsala University（乌普萨拉大学）；KTH Royal Institute of Technology and Stockholm University（瑞典皇家理工学院和斯德哥尔摩大学）；University of Geneva（日内瓦大学）；University of Turku（图尔库大学）；Aberystwyth University（阿伯里斯特威斯大学）
Observing weakly broken conservation laws in a dipolar Rydberg quantum spin chain
Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Université Paris-Saclay, Institut d’Optique Graduate School, CNRS, Laboratoire Charles Fabry（巴黎萨克雷大学、光学研究生院、法国国家科学研究中心、夏尔·法布里实验室）；Université Paris-Saclay, CNRS, Laboratoire de Physique Théorique et Modèles Statistiques（巴黎萨克雷大学、法国国家科学研究中心、理论与统计物理实验室）
