Quantum probability was developed in the 1980s as a noncommutative analog of the Kolmogorovian theory of stochastic processes . One of its aims is to clarify the mathematical foundations of quantum theory and its statistical interpretation.
A significant recent application to physics is the dynamical solution of the quantum measurement problem, by giving constructive models of quantum observation processes which resolve many famous paradoxes of quantum mechanics.
Some recent advances are based on quantum stochastic filtering and feedback control theory as applications of quantum stochastic calculus.
Read more about Quantum Probability: Orthodox Quantum Mechanics, Mathematical Definition
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