The triangle principle: a new approach to non-contextuality and local realism

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 defined as a lack of existence of a joined probability distribution giving rise to all measurable data. Therefore, we show that one can design Bell-Kochen-Specker tests using a different principle.