A superoperator is a concept primarily used in quantum mechanics and quantum information theory. It refers to a mathematical operator that acts on the space of operators (often density operators, which represent quantum states) rather than on state vectors in Hilbert space. Superoperators are essential in the study of quantum dynamics and quantum information processing, particularly in the context of open quantum systems and quantum channels.
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A linear map between spaces of linear operators. A physical quantum channel is a superoperator that is trace preserving and completely positive; a general superoperator need not have either property.