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We give an argument for strong positivity of the decoherence functional asthe correct, physical positivity condition in formulations of quantum theorybased fundamentally on the path integral. We extend to infinite systems work byBoes and Navascues that shows that the set of strongly positive quantum systemsis maximal amongst sets of systems that are closed under tensor productcomposition. We show further that the set of strongly positive quantum systemsis the unique set that is maximal amongst sets that are closed under tensorproduct composition.

An Argument for Strong Positivity of the Decoherence Functional