An Argument for Strong Positivity of the Decoherence Functional
arXiv:2011.06120 · doi:10.1116/5.0073587
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.
arXiv comment22 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 (14)
- A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
- Quantum Mechanics as Quantum Measure Theory
- On the Consistent Histories Approach to Quantum Mechanics
- Properties of Consistent Histories
- Quantum Measure Theory and its Interpretation
- Anomalies of weakened decoherence criteria for quantum histories
- The Random Walk in Generalized Quantum Theory
- On extending the Quantum Measure
- Generalizing Quantum Mechanics for Quantum Spacetime
- A histories perspective on characterising quantum non-locality
- Hilbert Spaces from Path Integrals
- Distinguishing initial state-vectors from each other in histories formulations and the PBR argument
- Composing decoherence functionals
- A "problem of time" in the multiplicative scheme for the -site hopper