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Quantum(-like) common knowledge: Binmore-Brandenburger operator approach

We present the detailed account of the quantum(-like) viewpoint to common knowledge. The Binmore-Brandenburger operator approach to the notion of common knowledge is extended to the quantum case. We develop a special quantum(-like) model of common knowledge based on information representations of agents which can be operationally represented by Hermitian operators. For simplicity, we assume that each agent constructs her/his information representation by using just one operator. However, different agents use in general representations based on noncommuting operators, i.e., incompatible representations. The quantum analog of basic system of common knowledge features ${\cal K}1-{\cal K}5$ is derived.