The axiom of choice and the no-signalling principle

Autor(en)

Amin Baumeler, Borivoje Dakić, Flavio Del Santo

Abstrakt

We show that the axiom of choice, a basic yet controversial postulate of set theory, together with one of the pillars of our best physical theories, namely the no-signalling principle, may point to a limitation in modelling physical problems using standard mathematics. While it is well known that probabilistic no-signalling resources (such as quantum non-locality) are stronger than deterministic ones, we show - by invoking the axiom of choice - the opposite: functional (deterministic) no-signalling resources can be stronger than probabilistic ones (e.g. stronger than quantum entanglement or non-locality in general). To prove this, we devise a Bell-like game that shows a systematic advantage of functional no-signalling with respect to any probabilistic no-signalling resource.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Università della Svizzera Italiana, Facoltà Indipendente di Gandria, Österreichische Akademie der Wissenschaften (ÖAW), Universität Genf, Constructor University

Journal

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Band

481

Anzahl der Seiten

9

ISSN

1364-5021

DOI

https://doi.org/10.48550/arXiv.2206.08467

Publikationsdatum

07-2025

Peer-reviewed

Ja

ÖFOS 2012

103025 Quantenmechanik

Schlagwörter

ASJC Scopus Sachgebiete

Allgemeine Mathematik, Allgemeiner Maschinenbau, Allgemeine Physik und Astronomie

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/d1a787cf-cf51-4631-bf46-9bde31c99c05