An Argument for Strong Positivity of the Decoherence Functional

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.

22 pages. This version submitted for publication in a Special Topic Collection Celebrating Sir Roger Penrose's Nobel Prize for AVS Quantum Science (AQS), eds. Ivette Fuentes Guridi and Hendrik Ulbricht. Results and proofs same as in version 1. This version contains extra text in the introduction and at the end of the final discussion section

References in corpus (6)

• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Generalizing Quantum Mechanics for Quantum Spacetime
• On extending the Quantum Measure
• Hilbert Spaces from Path Integrals
• Composing decoherence functionals
• A "problem of time" in the multiplicative scheme for the $n$-site hopper

Cited by in corpus (1)

• Decoherence and Probability