2013/09/26 by Paweł Kurzyński, Pawel Kurzynski, Kurzynski, Pawel +2 · 1 citation
Arts and Humanities · Physics and Astronomy · #FOS: Physical sciences #Philosophy and History of Science #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.1309.6777
7 pages, 1 figure
arxiv created 2013/09/26 · openalex publication_date 2013/09/26 · arxiv updated 2013/09/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.