The triangle principle: a new approach to non-contextuality and local realism
Pawel Kurzynski, Dagomir Kaszlikowski

TL;DR
This paper introduces the triangle principle, an information distance-based approach that simplifies the derivation of non-contextuality and local realism inequalities, highlighting differences between classical and quantum theories.
Contribution
It proposes the triangle principle as a new foundational approach to derive non-contextuality and local realism inequalities more simply and explores its implications for Bell-Kochen-Specker tests.
Findings
The triangle principle holds in classical theories but not in quantum theory.
It allows simple derivation of non-contextuality and local realism inequalities.
The principle can be used to derive monogamy relations.
Abstract
In this paper we study an application of an information distance between two measurements to the problem of non-contextuality and local realism. We postulate the triangle principle which states that any information distance is well defined on any pair of measurements, even if the two measurements cannot be jointly performed. As a consequence, the triangle inequality for this distance is obeyed for any three measurements. This simple principle is valid in any classical realistic theory, however it does not hold in quantum theory. It allows us to re-derive in an astonishingly simple way a large class of non-contextuality and local realistic inequalities via multiple applications of the triangle inequality. We also show that this principle can be applied to derive monogamy relations. The triangle principle is different than the assumption of non-contextuality and local realism, which is…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsQuantum Mechanics and Applications · Philosophy and History of Science
