An Argument for Strong Positivity of the Decoherence Functional

TL;DR

This paper argues that strong positivity of the decoherence functional is the correct physical positivity condition in path integral formulations of quantum theory, establishing its maximality and uniqueness among quantum systems.

Contribution

It provides a theoretical justification for strong positivity as the fundamental positivity condition and proves its maximality and uniqueness among tensor-closed quantum systems.

Findings

Strong positivity is the correct physical positivity condition.

The set of strongly positive systems is maximal under tensor product closure.

Strong positivity set is unique among such maximal sets.

Abstract

We give an argument for strong positivity of the decoherence functional as the correct, physical positivity condition in formulations of quantum theory based fundamentally on the path integral. We extend to infinite systems work by Boes and Navascues that shows that the set of strongly positive quantum systems is maximal amongst sets of systems that are closed under tensor product composition. We show further that the set of strongly positive quantum systems is the unique set that is maximal amongst sets that are closed under tensor product composition.