Are There Quantum Operators and Wave Functions in Standard Probability Theory

Abstract

The methods of quantum probability theory are radically different from standard probability as developed over the last 300 years. While the results of quantum probability, such as expectation values, are the same as standard probability theory, the methods used are strange, as they deal with operators and wave functions and use strange rules of manipulation. We ask whether there are operators and wave functions in standard probability theory. By generalizing a theorem of Khinchine on characteristic functions, we show that indeed the strange probabilistic methods of quantum mechanics follow from standard probability theory.